It's not just you. There are subtle differences in the way physics resolve each frame between the games. The short version of the story is that in the order of operations within a frame, Brawl/PM's engine updates character position before it updates their momentum, whereas Melee does the opposite. This means things that grant or change momentum would comparatively occur 1 frame later than they would in SSBM. An air dodge will stay in place for 1 frame before moving them in the direction of the analog stick on the 2nd frame. This generally doesn't impact how interactions resolve but certainly 'feels' different and is likely what you're noticing.
Otherwise, most of the changes are differences in input leniencies; SSBM's input windows for things like dashing, dashing backwards, shorthopping, and shield dropping are notoriously strict. PM's were made more lenient on purpose because it feels better. The SSBM community later adopted UCF to address some, but not all, of those issues in SSBM, namely dashing backwards and shield dropping.