Different title screens.
The character select screen features a slightly lighter background, a new world map, plus the select grid is obviously now bigger to fit the four boss characters in it, who can now be played as.
The Vs. screen was changed slightly, but the portrait artwork of each character was changed.
Many of the stages feature new colors in Champion Edition. Here is Ryu's stage, which is also now missing the sign posts at either side of it in Champion Edition.
Honda's stage.
Blanka's stage.
Guile's stage. It seems someone wanted most of the stages to now be set late in the afternoon, rather than the morning.
Ken's stage.
Chun-Li's stage. The people riding bikes have new sprites in Champion Edition.
Zangief's stage.
Dhalsim's stage.
Balrog's stage.
Vega's stage.
Sagat's stage, which no longer features the palm tree.
Bison's stage.
Many moves were changed in Champion Edition, such as Ryu's hurricane kick knocking opponents over. See the individual character pages for more info on what was changed for who.
In The World Warrior, Bison's win quote had a typo. This was fixed in Champion Edition.
Many of the endings feature slightly changed art for certain things. Gorbachev went from happy looking...
...to not very happy at all. Plus the sprites for Zangief and the secret agents were changed.
Eliza no longer looks like some evil killer mutant.
Ken still looks creepy as hell in both versions, though.
Some of the changes were incredibly minor edits, such as the dress Chun-Li gets rid of.
