Pretty much every port has something different that could be considered a new feature. I won't list games that mainly only have a CD version of the original soundtrack.
Sidearms Special: rearranged CD soundtrack, alternate BC version of the game.
Super Darius: new bosses
Super Darius II: new soundtrack, game is supposed to differ in other ways (I think its bosses again)
Bloody Wolf: has a whole new and improved soundtrack plus running and flying modes.
Street Fighter II CE: VS mode.
Golden Axe: cinemas and other new presentational features.
Double Dragon II: new graphics + cinemas
Altered Beast CD: intro 'cinema'
Strider: cinemas + 1 new stage
Aeroblasters: redrawn graphics + yellow ship intro + new stage 2 music + lots of tricks
Dragon's Curse: loses 99 Charm Stone warps, Tiger-Man, back-up saving, 60 fps.
Dynastic Hero: cinemas, new soundtrack, new character sprite, new bosses/characters.
Ys I - III: cinemas, new ingame character art.
Magical Chase TG-16: new sprite, new stage 1 bg, other visual differences.
Valis I & II: pretty much all different/new.
Popful Mail: enhanced visuals, new cinemas, voices.
Populous CD: Bomberman world.
Tiger Road: pretty much all different/new.
I don't think that Darius Plus added anything to the arcade version. Super Darius doesn't have new levels as far as I know, only unique bosses for each of the 26(
the arcade and Darius Plus recycled bosses).
Chuka Taisen is supposed to be an overall different game than the arcade original.
I've heard that Shinobi had a few levels taken out for the PCE version...
I believe that it is missing the bonus stages, unlike the rockin' SMS version.