Given that FFIV is, I think, just basically a worse game than III to start with, if you really didn't like III DS, I wouldn't bother, no.
FF3DS is a better remake than FF4DS, if you ask me, and I personally agree that FF3 > FF4 based off the originals. FF3DS mostly has one really major fuck up, which is the final dungeon bullshit (no save points; back during the NES era, this was more forgivable. But now? No, there's no excuse for a dungeon this long with no breaks and no save points. Especially when the final boss is NOT a trivial fight.)
Otherwise, it kept the general difficulty the same (horizontal shift basically; randoms are somewhat easier overall, but bosses are overall harder. The Dark Guardians not-Cerberus are the exception since they all are much worse than their Original incarnations, which is sad), and totally reworked the balance, such that every job for the most part can be used at any point its available, instead of "Ok, now you have Knight, NEVER USE FIGHTER EVER AGAIN!", so you have more options to work with, especially late game where the final dungeon is no longer "Sagex2 + Ninjax2 = Yay!" but you can actually make a team custom to your liking! (...so long as some form of adequate healer is among that group, unless you're a masochist or have FEOK's...who can heal anyway thinking on it...)
It leads to a different experience at least, for all that the core game is overall the same.
FF4DS did change the mechanics a lot meanwhile. Just compare the FF4DS Stat Topic to the FF4o/a one, and you'll get an idea of what I mean.
One thing FF4DS also did was really make apparent how FF4's story was NOT a masterpiece (for all that nostalgic fans will defend it to highest hell.) It tried to make epic scenes out of bland generic crap, and it only made the scenes look silly.
Just look at the scene in Myst. You know, a scene where a town is burning and there's a little girl crying over her dead mother...you'd think this should have some powerful visuals and audio. FF4o/a did a decent enough job considering the time, I suppose. FF4DS turned the scene into...more memetastic than anything. Cecil's yelling "WHY!!!!!!!!" certainly doesn't help, the scene feels rushed rather than just "oh, SNES game, ok" and Rydia's "I HATE YOU!!!!" really did not need that DRAMATIC ECHO, which actually made it harder to take seriously, rather than add emotional impact It really just made the scene sillier rather than improve it.
I will grant that the added Golbez stuff was nice, since hey, NOW GOLBEZ HAS BACKSTORY! That's something the ENTIRE FF4 CAST DIDN'T HAVE! The added flashbacks for Cecil/Kain/Rosa did absolutely nothing but tell us stuff we pretty much already knew, and were cheap. Honestly, FF4DS really just exemplified how poor FF4's plot is and how badly it aged, instead of actually fix up what was wrong with it.
Part of why I don't want an FF5 or FF6 remake is cause I don't think the remakes will necessarily be better than the core games, and to be frank, both games have aged considerably better than FF4 so they really don't need one.