Depends on the remake. For me, FRLG was not so much of an improvement because not many new features were added outside of updated mechanics (and Sevii islands, but I didn't really like those). I still play Yellow just for the nostalgia value. HGSS, on the other hand, was an amazing remake, and, in my opinion, by far the best one, and yes, I have not touched my GSC since. ORAS, on the other hand, took out all my favorite features from Emerald (imo the best game in the series), and I played it once and promptly went back to good old gen 3. Honestly, it's the difficulty value that is why I don't like ORAS as much as Emerald (still better than RS).
DP remakes will fix my one huge pet peeve, the incredibly long saving time, and, hopefully, be more like HGSS than ORAS or FRLG and take a page out of the third versions, as well as add new areas and content. Because, honestly, the only reason I don't play Platinum anymore is because of that slowness. Literally nothing else has to be "improved" if you ask me. Heck, GF could rerelease the exact same game just with better graphics and I would love it. It's just perfect that way.