The remasters got better with each iteration. The early TOS ones were gaudy and the altered frames really stood out, then they started to do them so they fit better and changes started more subtle, and a lot of the TNG ones don't really stand out if you've never seen the original episodes. They just look hott if you have an original to compare to.
Until
Enterprise (I think), Star Trek TV series were shot on 35mm film, so they're 4:3 by default (and the remasters are fairly easy), originally they were redoing the space scenes for TOS/TNG in 16:9 but they changed that to fit the episodes. DS9/VOY were thought to have too much CG with the original files lost to be worth the cost, but apparently they found the original CG files and were doing testing starting with just running the sequences at higher resolutions.
I believe when it came time for the DVDs they did another quick pass over the early TOS remasters to clean them up a little. But, unlike say, Star Wars, the updates always were mostly focused on making the matte backgrounds not stand out when seen in HD, redrawing them to be "true" to the original vision, etc.
Arena's a great example because who the fuck knows what's going in the background of that original one. (And it clips over the edge of the set.
)
Original:
Remastered: