There is a single thing VI does well - it has superb production values, is probably the finest crafted jRPG on the SNES, and definitely set the bar for the rest of the series. If you insist on comparing it to VII, then there's three points you almost certainly need to consider:

1) They both have approximately the same production values;
2) VI was developed towards the end of the SNES' shelf life, with an extensive library of games by Square behind it;
3) VII was developed at the beginning of the PS' life, and was their second title (first RPG) for that system.

VI and VII essentially have pretty much the same flaws when it comes to quality. That only means that VII is less forgivable, for reasons of experience and technological potential. You can argue about which looked better or sounded better all you want, though everyone's tastes are different and no point is made by doing so.

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Apart from that craftsmanship, though, there isn't much VI actually does well. To address the main points people like to say make this the best title in the series:

The story: strangely devoid of plotholes for a Final Fantasy title.

The (playable) characters: all but a couple are incredibly shallow and irrelevant to the story (due to interchangablility, part of the game design), having little development outside of their time in the spotlight during their initial recruitment as well as their re-recruitment during the World of Ruin. The three optional characters, Mog, Umaro and Gogo, have essentially nothing. Of the development the characters do see, none of it is irretrievably tied to the setting of VI, thus all but Terra can easily be transplanted into another game and lose nothing for it.

Example: Locke wants to protect Aeris from the Turks because he was unable to protect Rachel earlier. Later, he finds the Phoenix materia and unsuccessfully tries to revive her. Cyan is a slight stretch, Strago & Relm have some stake in the setting, but change them to Ancients/Summoners/Al Bhed etc. and you're good.

Comparing VI to V is fine, but you oughtn't fall into the trap of comparing V's story to anything. It's good, but only in the context of an excuse plot, being remarkable only for being very aware of that fact (later less successfully attempted in X-2). My favourite description of V's story:

FFV's story is literally this:

One time a tree hated people so much he became an evil wizard
But four warriors defeated him and sealed him away
But he got out and now you have to defeat him
Also your dad's best friend was a werewolf.
V is definitely a superior game to VI, even considering the craftmanship and story of the latter, and it's overwhelmingly based on the comparison of gameplay of the two. The gameplay of VI is completely, utterly vapid. Set character classes were a regression even when VI was new (fun fact I just realised typing this: NES era FFs were more progressive than SNES era FFs), and the sheer number of characters and immense freedom in party building are at best a poor-man's version of V's job system.

Even considering most FFs before and since could be broken by some basic means, there remains no actual reason in VI to break the system. Compare to 8, which no one is going to dispute has the most breakable system in the series, can be powergamed to the max and you'll still need to find a way to deal with Omega Weapon. VI's answer to this is simply asking you to surrender control of your characters, and those who disliked XII because of the Gambits system will be quick to tell you how horrible having a game play itself is.

TL;DR yes VI is overwhelmingly overrated.