While (to my knowledge) it was never directly addressed in-universe in so many words (i.e. you will not find an explicit reference), you have to keep in mind the context of what the Jedi are doing:
In Episodes I-III, the Jedi spend a lot of time... sitting. And meditating, sure, but while that may improve their connection to the Force and ability to use it, it's going to hurt their physical ability (which we know from various C-Canon sources is important as well, not least because the more honed their physical reflexes are, the more they can devote their mental focus during a fight to using the Force rather than deciding which way to step1). To be sure, there is training going on -- and we certainly see some impressive fruits of that training -- but outside of that they're still doing a lot of sitting.
In The Clone Wars, however, when they're not training, they're fighting a war. That's going to hone their reflexes and improve their physical fitness quite a lot (and not only because those who don't improve get dead). We see the same effect in the real world -- soldiers who are serving outside of war zone may be fit, but send them into an active combat situation and their physical fitness and reflexes improve dramatically. Not at all unexpected when you consider things like running around with 60-pound packs while taking fire and shooting back. (Sure, the Jedi still spend time sitting during this time, but the whole fighting a war thing severely cuts into their leisure time -- wars are awful inconvenient like that.)
(Note: The sitting-vs-fighting a war thing is a deliberate over-simplification to make a point. Yes, Jedi do more than just sit around, but so do real-life soldiers and yet you see the same marked improvement in physical prowess when a soldier is sent into an active war zone. [Source: First-hand knowledge, i.e. I've seen precisely this among soldier friends training at home, and then seeing them freshly back from a tour or three in the Middle East.])
In Episodes IV-VI, we see:
- Obi-Wan: An old man who, despite his strong connection to the Force, is just getting too old for this.
- Yoda: Even older than Obi-Wan! And he stands in very marked contrast to the nimble little muppet we see in the prequels, all but proving this point that he's just gotten old. (That said, though, we never see him in a context where acrobatic feats would be expected, so...)
- Vader: Most of his body isn't even his body any more, and while the cybernetics seem really danged good that's going to impair his physical ability and prowess. Not to mention that he's gotten into the whole Jedi sitting thing (well, okay, he seems to stand mostly, but similar effect).
He was never (to my knowledge, anyway -- haven't seen all of Clone Wars) an agile combatant I forgot about his duel with Yoda in the prequel trilogy, but nonetheless he's primarily a manipulator behind the scenes (presumably far more so once he had an entire empire to do his bidding), and in any case by these films he's taken the Jedi sitting thing to a whole new level!
- Luke: Brand new to this whole Force/Jedi/etc. thing. Naturally you can't expect him to match the physical prowess of life-long trained Jedi like Obi-Wan at his physical peak. He still pulls off some impressive acrobatics despite being so raw, in excess of what the others can do, but he's also more youthful and energetic than all the rest as well.
That said, even though all of this is so plausible to the point that anything else would strain credulity, I suspect the real reason is the out-of-universe one: Clone Wars' Jedi are more acrobatic because pure-CG can do a lot more; Eps I-III are next because modern technology let them do a lot more than they could in the originals; and finally Eps IV-VI are relatively limited because the technology was relatively limited. As well I strongly suspect that the long-running nature of Clone Wars contributed to a sort of "power creep", where Jedi necessarily had to get more and more powerful/impressive to keep viewers, well, impressed.
The different canon "levels" don't present a "legendary" vs "realistic" depiction of the Jedi; rather, they exist to acknowledge that Lucas, as the legitimate "owner" of the universe, is the only one with final say in what is and is not part of his world (G-Canon); the TV shows (T-Canon) add to it, and are considered "higher" than the books etc. (C-Canon), because of the closer adherence to Lucas' expressed vision. [Yes, this paragraph ignores that Lucas has sold Star Wars to Disney, but Disney in turn has declared everything below T-Canon is no longer canon at all, while simultaneously folding G- and T-Canons into a single, unified canon. Thus any discussion of canon levels implicitly also ignores this transfer of ownership.]
1 Stated multiple times in e.g. Path of Destruction, during any of the myriad lightsaber training sessions; granted that's specifically noted within the context of training lightsaber styles and sequences, but the principle is obviously applicable to other physical feats as well.