Great thread! I love these comparisons thread because I often owned multiple consoles of the same generation and was always at a loss when trying to choose a multi platform game.
From the first few pages (based on not just screen shots, but trying the game either in person or via emulators)..
Tokimeki Memorial - PC-Engine hands down. The SFC has smoother blending of colors and gradients, that is for sure. the SFC chip music sounds better than the times the PCE uses its chip music. But at the end of the day, Tokimeki Memorial is a game that highly relies on its anime style story telling. The PCE version has a larger resolution, animated scenes, more sprite animation, etc that tells the story better. Also note that in many background images on the SFC, the locales are empty. Looks like people are dating in a ghost town.
Emerald Dragon - Back when I did romhacking, Emerald dragon was a game I wanted to translate, but couldn't due to limited skills. I'm glad some one else picked it up. I thought it had really good graphics that reminded me of an SNES Enix game like Terranigma or Illusion of Gaia, more so than a Square game (this was before the merger). Then I learned of the PCE-CD version. In pics it does look the SNES/SFC version is better with more details, but when playing the PCE-CD version and watching videos of it.. the PCE-CD is also good. The different use of colors gives it a different feel, despite similar lay outs. It reminds me more of a late end Genesis RPG like Shining Force 2. Overall prefer the PCE again. The graphics advantage over the PCE is not that huge and in fact I'd say its apples to oranges. But the PCE has better music, animation, voice acting, etc that tells a better story.
Art of Fighting: I'm going to start by saying Takara often did lazy ports of Neo-Geo games to the SNES/SFC. Take a look at John's stage in the SNES version. The helicopter looks awful and lazily drawn. The floors are also awful. The only bright side to the SNES version is smoother scaling and the music. While Takara did a sloppy job on graphics, they often did remixed versions of the music for the SNES versions. Some were so-so, but some were superior to the original. For example Mr. Big's stage.
The PCE version has the best graphics of the 3 16-bit home ports. Also the best music. But that zoom is awful. The Genesis version also had better graphics than the SNES version, and it had better animation and even incorporated parallax scrolling not in either two. But the voices were awful, and the music just so-so. However I liked that it didn't use the zoom feature. Overall I'm going to say a tie between the Genesis and PCE version, SNES last.
World Heroes 2: The SNES version has better voices and sound effects. PCE with larger sprites and it seems more animation. Music is better too. I think I'll give this to the PCE
Parodius: This one SNES hands down. Better music. Graphics are pretty comparable overall.