An episode early in Season 3 of Battlestar Galactica has a shaman-ish person tell the Lucy Lawless Cylon that she will indeed hold The Special Baby in her arms. By the end of the episode that happens.
In the very first episode of Babylon 5 (after the pilot) Londo has a dream that he and G'Kar will strangle each other to death. This makes sense because not only are they fighting each other but they're more or less trying to wipe out each other's race. The dream comes true but it's a couple of seasons later and when it happens means something entirely different than what we originally thought.
This moment in BSG is when I realized just how much the show is if not exactly picking up pieces from B5 then following on ground it had cleared. The difference is that B5 is a richer, more complex show (at least so far - I have a season and a half to go of BSG). In this example I still have no idea why BSG had this little prediction because it means nothing and as far as I can tell doesn't hint at anything greater. It's almost like the BSG creators said "wouldn't it be cool" but didn't think it through. In B5 how the characters move from hatred to their final stage is one of the main stories of the show and thematically parallels the other stories. It's also structurally a strategy frequently used in B5 where a few times we're told what will happen but it's not quite as we'd expect, or more broadly and commonly times when a character changes or reveals something over time. (There are too many of the latter but some worth noting are the comic-relief character who turns out to be the first to stand up to the Shadows, the loyal aide who betrays Sinclair in a moment of weakness, the closest to an actually "evil" person Bester revealing something from his past.)
What else did BSG draw from or at least echo B5? The military vs civilian authority conflict (in fact a major theme of B5 is the proper use of authority and who is able to claim it), the focus on religion (though I'm still not sure where BSG is going with this but B5 is more varied and realistic), an alcoholic character (but then this is a go-to problem for lazy writers - though again B5 focused more on the struggle while BSG seems to have just switched it on and off as needed), the conflict of possibly misguided secret police (in BSG the New Caprica human police story is resolved in a couple of eps but B5 takes the Night Watch story much longer and to some degree more morally complicated) and more. BSG even has an ep where one character thinks that they may have triggered the Cylon attack but then they're let off the hook because it was clearly "thousands" of things that created that result. B5 brings on the person whose misunderstanding caused the Minbari War and thereby almost completely wiped out the human race - in the B5 world nobody gets a last-minute reprieve. (Clearly the BSG creators could have come up with this idea without ever even having heard of B5 but the basic idea is so similiar that it seems almost like a cop or an hommage, depending on your view.)
But there's another area where I'm surprised BSG falls below B5 and that's the background and the supporting characters. In BSG we get the initial Cylon attack and bits about the previous conflict but that's about it. BSG has about a dozen main characters with only a few others appearing from time to time. By contrast in B5 we know a lot about the Minbari War which ended before the show starts not to mention the Narn-Centauri conflict, the history of the other Babylon stations, etc. There are also numerous other characters, some who appear very briefly for a specific plot point but others more frequently for other purposes. (One of the most interesting is the Minbari warrior Neroon who appears in just a few eps - initially he's a source of conflict but in a nice bit of writing comes around to the other side without really changing character.) B5 also had a few "gimmick" episodes - many series have an ep done as a news report (MASH for instance). But some of B5's most memorable are these gimmick shows - the one told from the viewpoint of two maintenance men, Neil Gaiman's "Halloween" ep and definitely the last ep of Season 4 (the one that has sections set 100, 500, 1000 and a million years after the main story). BSG mostly avoids the gimmick eps or in one case (the boxing ep) badly botches it.
I think there's a reason for this and it relates to why BSG gathered such acclaim while B5 will remain underrated. BSG was created by TV writers who happen to like SF but B5 was created by a SF fan who happens to be a TV writer. So Straczynski wrote "real" SF - densely interrelated, deep backstory, morally complex. The BSG creators streamlined all of that - fewer characters with a simpler story and only a few sidestories. It feels like no accident that BSG's "other" look completely like humans (with the metal Cylons rarely appearing). Altogether people who don't like SF (or aren't willing to try it) can feel like they're open-minded by watching a SF show while mostly seeing it as an unusual war series. No having to deal with B5's lizard people, Renaissance-excess-looking humanoids, sentient insects, mist people, cyborgs, psionics and so forth. Viewers can also watch an ep or two of BSG and get some of the gist of the show but for B5 you have to watch much more. Much of B5's main point doesn't come together until the end of the first season (on purpose) and it takes nearly the entire show for the full architecture to come out. As I pointed out before B5 is a show where change is the main point - if nothing else the big conflict appears to be familiar Good vs Evil but eventually turns out to be something quite different. I still have hopes that BSG will surprise me and come together towards the end but at the moment am not too hopeful.