On the comparisons between these two shows, I'll be discussing some of the ways they're similar and some of the ways they're not. It's pretty clear where 12 Monkeys got its inspiration from... but it feels more like Battlestar Lite to me, and I believe this is reflected in these repeated phrases on both shows.
In Battlestar, the phrase didn't make much sense until much later in the show when we found out *suchandsuch* whereas with 12 Monkeys, we pretty much know the phrase is talking about time itself, so it's pretty self-explanatory. It's simply attempting to be more "prophetic" than it actually is.
There's also an ongoing philosophy and attention to character interactions given to every scene in Battlestar Galactica. There's certainly no shortage of plot or world-building happening on BSG, but these are all woven in seamlessly while we're given a chance to relate to these characters.
In 12 Monkeys, the plot comes first, and the character interactions are serviceable, but they serve no greater purpose other than to add "drama" to the show. You could say Cole's relationship to Dr. Railly is like a slow burn leading up to a romantic creciendo at some point in the future (or the past?), but their relationship really has no arc to it. It simply goes through bumps and dips, peaks and valleys, but there are no high or low points to them. I think the biggest hurdle in relationship turmoil was between Cole and Jose, given what happened between them. There was quite a huge, HUGE event that should have changed things between them forever, but it didn't. In fact, you could say things returned pretty much to normal... and this is why I feel like 12 Monkeys is sort of a "whatever" kind of show.
In BSG, relationship arcs form a huge basis for the underpinnings of much of the show. You could still play out all the things that happen on BSG, beat by beat, but without that depth of character interaction, it would feel like a very cold show to watch. These character interactions, and the original way in which the show is told to us, the creative uses of storytelling techniques, through music cues and the symbolism of Caprica 6 in a red dress; the seduction of telling a lie. There's so much richness to the show that it's impossible to really understand everything that's going on the first way through the series.

In forming the prophecy for BSG, the creators took their time fleshing out the universe and dropping hints throughout the episodes. There sometimes wouldn't be a hint dropped about this prophecy for 3 or 4 episodes. And hell, I don't think they even really knew exactly where things were going to end when they first got started. They just kept the ball rolling until they figured out they had an ending in sight. I think this method was the best, because by then it gave people a chance to get invested in the mythos of the world. The only downside was there was never going to be any pleasing way to end it for the fans.
But with 12 Monkeys, they feel it necessary to drop hints about this prophecy every single episode, and you could say it's the entire plot of the series itself. The primaries, the travellers, the witness, the 12 "monkeys" themselves... It's all part of the same plot, and it's incessant. There are no times where Cole and Dr. Railly just relax and have dinner to discuss who they are as people in context of the plot. That's just not what this show's about. This show is about the constant oncoming of future events and poking us into wondering how things will play out... That's HOW things will play out, not necessarily WHY. And that's a big part of my problem with this show.
I guess the ultimate question is, does that make 12 Monkeys a worse show than BSG or is it as good but in a different way? Well, for me, it makes it seem like a less bingeworthy show, like I could more or less live without it. I watch it in a very sparse manner, because there are no emotional beats to keep me invested. With BSG, I remember binging the hell out of it, and I often couldn't help but move on to the next episode. I must have binged like 6 or 7 episodes in a row back then. They teased you just enough with each episode that it kept you wondering how things were going to play out in the next ep.

Now obviously it's not just the character interactions that gave BSG its succulent, sweet flavor. That had a big part to do with it, but it felt more to me like a perfect confluence of talent; Bear McCreary was the composer (The Walking Dead), and the score to BSG is just phenomenal. It adds emotional impact to every scene, and I very much doubt one could make it to the end of this series without having cried once. The showrunner, Ronald D. Moore, told the story of this show like an art piece. Sure, it could get a little pretentious at times, but you always felt like you were in capable hands, like he was leading you somewhere awesome... and it was awesome.
But if I really had to tell you what made BSG one of the greatest shows ever made, it would be Theme. Theme in this instance meaning "the entire point of the story," or the "meaning" of a story. It's very difficult to weave in theme alongside plot, because much like life, there really is no meaning to anything we do in life. We extrapolate meaning, and that's how we find purpose in our lives. With tv shows, books, and movies, the theme needs to be presented to us much the same way. It does not come prepackaged with any story we tell; we have to figure out the meaning of the story and how that relates back to us.

With BSG, the clever decision to make cylons basically human is essentially an allegory to racism, which we still face in the real world. I think this is perhaps the truest intention for science fiction, because it shows us a world where things should be advanced and utopian, but we find that things are much the same. There are also themes of lust, greed, power, love, jealousy, rage... All these things are woven into the characters themselves, and they manifest in the plot. I mean, you couldn't have Gaius Baltar relinquishing power over to the cylons for the entire human race without his incredible desire for power and adoration; his ego drove that decision, and it was a driving force for the rest of the series.
I mean, even with a show like Quantum Leap, which is about as cheesy as it comes, had that emotional investment where, in the pilot, all he wanted to do was talk to his dad again, since he had died years ago in his own time. It gave the events surrounding the show that personal touch which kept all of it from feeling pointless. In BSG, everyone has a personal connection to something, or someone, and you can feel it coming off the screen, it's so palpable. Whether it's lust, or disgust, or admiration, or affection, we can feel those emotions in every interaction... and this drives the Theme home.

Getting back to 12 Monkeys, it's a decidedly smaller scale show, except it's dealing with even greater numbers of people. The extermination of 7 billion people is no laughing matter, but the ways in which they deal with trying to alter the past feel like two clubs bickering back and forth with each other. There are constant "flashbacks" (if you want to call it that) to different time periods in telling the story.
In discussing the Theme of 12 Monkeys, there really isn't much to speak of. You could bring up the obvious, such as wanting to "save billions of people," or "righting the wrongs of the past," but these sorts of themes aren't relatable enough for me to really get invested in their exploits... We know that Dr. Railly has lost her old boyfriend, Katarina has lost her daughter, Jose cares about his son, and Cole lost his dad... Well, none of these relationships are fleshed out. At all. These characters don't really have enough emotional motivation to keep time traveling, and it's really only due to the plot that it keeps moving forward. Things happen because they need to happen, and there is never a point where I'm going, "Okay, so how's this going to affect the next episode?" Everyone is pretty steady and predictable, so I know the next episode will just give me more plot to move the story forward.

Characters might be given some brief background stories, or allusions to people they've lost, but we really have no way of knowing what effects these events had on these characters. There is one bit where Katarina talks about "fate" at the end of the first season, and we find out through a "flashback" to 2015 that her past self never believed in fate; she was more objective and focused. I think this was only a phase, though, because a scientist who believes in fate probably wouldn't go on with her time travel project, so that bit of character development seems to have been lost in the wind... but this is a good example for how character development exists in this show; it's mostly cosmetic and temporary, because the real thing being prioritised here is the plot.
In this latest episode, the tension between Jennifer and Dr. Railly is finally released because she discovers that Jennifer is quite a sick, troubled young girl. Dr. Railly seems to finally soften her demeanor and starts to empathize with her, a return to the softness she once had in season one. This was a welcome interaction, because it showed us that Railly still cares for people, and that she has the capacity to feel regret for how she treats people.
This sort of depth in character is not explored nearly enough in 12 Monkeys, and I feel that these are the things people will come back for. That said, I fear that it will just come and go, and when it's gone nobody will miss it. Which is a shame, because they already have some interesting characters and a great premise. They just need to really dig in deep with it.
Battlestar Galactica built a world and a mythos so unique and incredible that even I know that it's unfair to expect every sci-fi show to live up to it. They can try, but they'll never quite reach those heights again.