I think the Classic setup of almost 5 supply centers per player works really well for variants of 7 players or more. I think a setup of between 3.5 and 5 supply centers per player is good. You want the possibility of large relative swings in supply center counts, you want tactics to play an important role and you don't want the end game to be a slog, so you don't want the number of supply centers per player to be too high. At the same time, you also don't want the possibility of players straight up being defeated after a stab with no chance of coming back, so you also don't want a gimmick setup of e.g. 1 supply center per player.

Unfortunately, many variants have too many supply centers for my taste. Especially the variants with a large number of players can become a slog if the number of supply centers is too high.

The couple of variants that do have the number of centers that I like are hard to balance, and most of them indeed are unbalanced. For instance, I like the idea of https://vdiplomacy.net/variants.php?variantID=114 but Rus is clearly unbalanced. I like https://vdiplomacy.net/variants.php?variantID=2 as well, but it is very unbalanced, too (and pigeon holes many powers into doing specific things). I tried to improve on it with https://vdiplomacy.net/variants.php?variantID=129 but in hindsight I am unhappy with what I did to Antarctica.

However I think Fantasy World Diplomacy (https://vdiplomacy.net/variants.php?variantID=44) is very well balanced. One might think Hamra and Rajasthan are too weak, but I believe that is just due to weaker players irrationally targeting them. I think these countries are stronger than Austria would be in Classic without a developed meta. So Fantasy World Diplomacy would be my vote for an underrated variant.

Came to the comments looking for Alcavre, wasn't disappointed.

Kievan Rus is so screwed in Crusades 1201. In hindsight changing the fleet to another army and maybe adjusting the borders with Hungary would probably work better.

I really like the map for dark ages, I don't know how balanced it is though

https://www.vdiplomacy.com/variants.php?variantID=82

The map’s a bit crowded, and the rules may seem complex (but really aren’t too difficult), but my whole regular group of variant explorers was really impressed with:

13th Century Mongolian Empire
https://www.vdiplomacy.com/variants.php?variantID=138

I’d also strongly concur on Fantasy World.

I’m also a fan of World Diplomacy, think vX was an improvement, but would agree on the Antarctica comment.

I also enjoy the simplicity of War in 2020
https://www.vdiplomacy.com/variants.php?variantID=61

and the strategy of Who Controls America
https://www.vdiplomacy.com/variants.php?variantID=43

The rest are either newer and growing at a good clip in games played here, or well over a 100 games played here.

I think Haven is put down a bit because it is fairly imbalanced for a variant requiring 20 players, but I think its mechanics of public supply centers and a central fast travel location are pretty fun. It would be fun if future variants expanded on the idea.

https://www.vdiplomacy.net/variants.php?variantID=51

Haven has a special place in my heart.

I've been playing Dark Ages and it's pretty good!

Germany 1648 is an excellent, very underrated variant.

Seconded. Really complex to think about knights and flips a lot of standard diplo (push forward in uniform lines amphibiously) out the window in favor of an all out get-what-you-can approach (see https://vdiplomacy.net/board.php?gameID=60301#gamePanel war between Spanish Habsburgs and the Ecclesiastical Lands)