After playing Pulse, Pure feels very strange, that's true.
But play it an hour and you get used to it. Actually it feels more WipEout than Pulse does because the ships slide more.
Dead-stops and roof-grinding are a bit annoying, though. But you can avoid the roof thingie (most of the time) if you know the tracks.
Overall, Pulse's handling is too direct to me and sideshifting shifts too much and turning turns to much (like if you want to correct your line you directly turn 30°).
Pure's far better at this point to me.

Then (in my eyes) Pulse never reached Pure's variety of track layouts and environments. The tracks look very similar in Pulse and don't seem that unique. There are exceptions like Vertica and Tech de Ra, but most of the tracks look rather uninspired to me (compared to Pure).

Pulse is a really good game, but, at least for me, it never lived up to the expectations. There was too much hype probably.

I just put Pure in my UMD drive again and I'm enjoying it very much (love the menus). If the game just had difficulty levels and online play.