Which game has the sleekest, most modern engine? Hmm, that's hard to say. I often find that games which tout an "engine" don't really have anything as intricate as an actual engine. The word engine brings to mind lots of gears and other moving parts all beautifully synchronized in an adaptable way.
For this challenge question I'll go with Albedo: Platinum Catalyst.
One of the things I liked right off is that to create a character you start with picking species (yes, it's a "furry" game). Then you choose a homeworld, and then you choose a personality. Yes, you choose a personality. The stats are Body, Clout, and Drive, which area nice break from the typical D&D style (or D&D derived) stats. All characters (or really "all personnel", since it's a military game) also have a Social Political Intelligence index rating. This is not only something on your character sheet but an actual in-game rating for your character. Your starting military rank and later promotions (and demotions) are based on this SPI.
There is not only physical combat (Body), but social combat (Clout), and psychological combat (Drive). I rather liked that there were three different types of "combat" built in. And since your SPI is calculated as 10 + Clout + Drive, social and psychological "damage" has additional consequences.
Anyway, of the games I've really looked at I would rate Albedo: Platinum Catalyst as having the sleekest, most modern engine.