As for that YouTube video, I don't see any material difference between the original shot choreography and this version.
Well quite, I was pretty baffled by the whole thing. Why bother if you're just going to replace the models with inferior CGI?
I actually don't think the battle needs to be more "dynamic" or exciting - the whole point is that the Enterprise-D is protecting her predecessor, taking the fire from the Klingons. If she were trying to defeat the enemy, I imagine there would be more evasive manoeuvres, but they would leave the Enterprise-C exposed and vulnerable to a couple of shots from the Klingons. Picard is essentially making his ship a sitting duck, as long as the Enterprise-C can get back into the rift.