IMO, Stephen Agar was right in saying: "I have no hesitation in saying that most variants are crap." in his "A Call to Arms against Crap Variant. Though "unpolished" might be a more apt term.
I've always admired 1900 and Ambition&Empire. Those are my favourite variants other than my own.
For one, I consider 1900 superior to Standard Diplomacy (and many familiar with both do agree). And Ambition & Empire introduced the Diplomatic Points mechanism, which brings so much extra nuance to the table, if you ask me. Got a few reservations about some aspects of Amibition & Empire's current version, but nonetheless I hugely admire this design.
An honourable mention would go to Diplomacy Royale. I find the concept incredibly interesting.
I quite like a number of others, but not really to the extent that I'd be dying to play 'em.
As for Ancient Mediterranean, well, I remember playing in one game years ago. I found it utterly bland and really should have known better than to join.
I think the basic circular arrangement of five powers is a problem. I think adding 2-3 northern powers. Say the Celts/Gauls,. Germans and Sarmatians would spice things up a whole lot.
Short of such a redesign, I think Ancient Mediterranean's victory conditions ought to be significantly lowered. The 50%+1 thingie doesn't make for a compelling game, imo, with so few powers.
I think in that respect Hundred got it right. A low victory condition can make even a three-player variant work. At least if you have three good players, who are up to a permanent rebalancing effort.