After Q3 almost all arena shooters and every new quake was based heavily on that same formula. I think Q3 is great but the success of the Q3 formula has been long exhausted in the arena FPS genre.

Quake 4:
Has the same weapons and almost the same weapon balance as Q3. There are a few unique characteristics, most notably the crouch slide, but Q3 theory is mostly reapplied.

Quake Live:
Basically a free version of Quake 3 but with nerfed weapons and some really ugly movement mechanics added on top (IMO)

Quake Champions:
It has champions but underneath that it's still the same Q3 formula.

One major exception was Painkiller, which had an entirely new movement system and new weapons. Unfortunately that game didn't play very well online.

If id ever wants to reuse a past successful formula in Quake again, and I know it's a big if, then how about a new Quake World? :) Only the movement has been redone so far.

I haven't played Diabolical yet but I personally hate the cell shaded look.