Which gaming system has the best mechanics and why?
I particularly want to know which d20 system has the best mechanics over all, conducive for theater of the mind and robust for balance. - But also interested in alternative systems like 3d6 in AGE, d100 in Eclipse Phase or differently the d100 in Marvel, and other kinds of systems.
For mechanics who has the best?
Probably the wrong forum for it. System mechanics and opinions about them get very esoteric. AFAIC, no d20 system is even remotely in the running for 'best system.' Like D&D, d20 succeeds because of the association with the first RPG, and the large cohort of RPGers who started with the D&D fad of the 80s and find the system familiar. It's really a pretty weak core system. It can't handle most genres, and doesn't do the one's it was originally developed to do particularly well, either. It's clumsy, list-based, archaic and collapses under it's own weight if you add to much to it. The flagship d20 game, D&D, is loaded down with baggage from the early days of the hobby, and that tends to drag down the whole d20 paradigm, as well. That doesn't mean there aren't good games that use the d20 system, or that you can't run a great game using one, just that the system, itself, in the technical sense, is not the what's making the game good or the campaign great.
Best system gets personal, too, because it depends on what you want out of the system. Personally, I think the best system must be universal. That's just a necessary requirement - if it's to be the best system, it must be able to do every kind of character, facing every kind of challenge, in every genre plus genres that don't even exist yet, /without/ adding rules to the core. With that as a minimum criteria, the only candidates are games so rules-lite they barely have systems - or Hero System, a rules-heavy, inaccessible, contraption that started as the superhero RPG, Champions! and went 'universal' from there.
Since I have to consider freestyle or excessively rules-lite 'universal' systems a cop-out on the system side (though they work great as games, if that's your style), I still have to give the nod to Hero System - probably the 4th edition of it, from 1989 - as the 'best' system, in the mechanical sense. The problem I have with Hero is that before 4th edition, it wasn't universal, it was a core system (like d20 is now) with a half-dozen or so games adapting those core mechanics. Starting with 4th, it became universal, but, by then, the skill system had already become bloated and open-ended, and was really starting to be a drag on the system as a whole. So, while the 5th (and, I've hard, 6th) editions are more refined in some ways, they're only getting worse as the skill system runs out of control. JMHO, sorry if that offends some current-ed Hero fans.
I particularly want to know which d20 system has the best mechanics over all, conducive for theater of the mind and robust for balance.
The best-balanced/most robust d20 system was probably D&D 4e, though I haven't tried all of 'em. The AEDU structure and the general design philosophy behind powers/items/features/etc meant that PCs didn't vary wildly in /relative/ effectiveness with campaign variables like pacing or nature of challenges - that's remarkably 'robust' by d20 standards.
The most conducive for theatre of the mind of the d20 systems I've seen is certainly 13th Age: it's specifically designed for that mode of pay and handles it very well (better than 5e, for instance), without sacrificing options. It's balance isn't too bad, though not exactly robust - it's maintained with a heavy-handed mechanic in which the DM decides when 'daily' resources re-charge, most of the time every 4th encounter, IIRC.
Dont forget the other half of the question ... ‘and why’.
