I only really remember the introduction videos for Black and R/B/FR/LG so it's hard to judge them on that.
The start screen of HG/SS and the original R/B are pretty cool in their own respects, the 3D Lugia/Ho-Oh was good while the random pokemon appearing beside Red was also cool so these are much better than the other start screens for me.
Then you're basically in to the professor introduction and it's the same for every game so not much choice there. So I guess purely based on the fact I remember its intro and like its start screen, it's the original R/B for me. Plus I love the classic Pokemon theme played in the intro and start screen on R/B.