Mostly it's standard Quake - same weapons (although the Grenade Launcher has disappeared), same power ups, strafe jumping, etc.
The physics appears to mostly be the same as Quake 3, but the maximum speed you can get through strafe-jumping has been capped (it's still fast, but I'm not good enough at strafe jumping to "feel" the cap).
As far as I can see, health and armour "overcharging" can only go 50 points above your regular maximum. For those not familiar with Quake, traditionally your "maximum" health and armour is 100 for each, but some health pickups (and all armour ones) can take you "above" your maximum, up to 200. However, your health and armour will slowly decrease back to the regular maximum (encouraging you to maintain control over the pickups).
The most significant deviation from the "classic" Quake formula is of course, the addition of distinct "Champions" with unique abilities, following the latest trends in online gaming.
I'll be honest, I was one of the *many* people quite skeptical with the idea of "heroes" in Quake (distinct characters with different stats and abilities), but I do think it's been implemented quite well.
Some of these passives bring in features from other Quake iterations - Slash gets Quake 4's "crouch slide", Anarki gets air control from the CPMA mod, and Visor gets an uncapped strafe jump.
The difference in starting health and armour between champions is significant - Anarki, a squishy character, starts with a measly 75 health maximum, and starts with 25 armour (50 maximum) - compare that to Sorlag, a veritable tank, who starts at 150 health and 50 armour (100 max)! The tradeoff is that Anarki is quite a bit faster, having the higher speed at 320 (the vanilla Quake speed I believe) vs Sorlag's 280. Nyx is the fastest character with a speed stat of 330, 300 seems to be "average".
The game mods at the moment are classic Deathmatch, 4v4 Team Deathmatch, 1v1 Duel (pick three characters, lose one when it dies, when all have died, lose the round, best of three rounds), and the new 4v4 "Sacrifice" mode. It's this last that will be the "official" competition mode and involves picking up a power up, moving it to your side of the map and "holding it there" for a while to score a point. I've only played this once, so I can't really comment on it. Mostly I've been playing TDM, like the dirty casual scrub I am. The UI shows slots for several other game modes, so more will likely be coming.
Most of the characters seem to be getting use (with one exception), although there is definitely a bias towards Anarki and Nyx, both fast characters with some unique movement options; Nyx has a walljump, allowing some quick shortcuts without having to rocket jump, and Anarki has his air-control.
The game is set to be "Free To Play", with payment for character unlocks. It is possible to "rent" a character, where you pay in-game currency to gain access to a character for 24 hours.
The starting character, Ranger (protagonist from Quake, and the only id software protagonist in the game so far), is pretty good though - he has a standard max 100 health and 75 armour, and the top tier 320 speed (beaten only by Nyx), his passive isn't too interesting (reduced self-harm), but allows more rocket jumping, and his active ability is a projectile that does quite a bit of damage (similar to a rocket) that he can teleport to (presumably he recovered the thing he used to kill Shub-Niggurath).
All I wish for now is for them to replace the stitches in Anarki's mouth.