tl;dr: What does Zandronum have that modifies the game's experience in oldschool doom gameplay?
Although there are numerous differences in the client/server code and how latency compensation, interpolation, and other bits of smoke & mirrors that ports use to try to hide the effects of latency, your post does specifically mention "oldschool" so I'll focus on that aspect alone.
IMO, a true oldschool experience would be one capable of exact fidelity with vanilla Doom. To that extent, an oldschool-flavored port should be able to play the vast majority of vanilla LMP demos perfectly to emulate the little quirks, bugs, and nuances of vanilla Doom.
The three major client/sever (c/s) ports are all based on different versions of ZDoom, which has notably diverged from vanilla Doom compatibility in favor of a perhaps a more modern game feel. Zandronum is based on the 2.x versions of ZDoom where as ZDaemon is based on ZDoom 1.23b33 and Odamex is based on ZDoom 1.22 with 1.23b33 physics. All three ports make some attempt to offer some degree of (toggleable) vanilla feel beyond what they inherited from ZDoom, with Odamex being the closest (it can play vanilla LMP demos), ZDaemon being second, and Zandronum being a distant third.
Some key differences you'll find between Zandronum and vanilla Doom are the physics and the weapon damage.
Zandronum has a different vertical spread for the SSG and a different method of calculating the damage per pellet. Some competitive players complain that this SSG feels too weak, but that is hardly conclusive. ZDaemon does not have the same spread or damage that vanilla Doom does, nor does it appear to be the same as ZDoom 1.23b33, however it is closed source and no further information can be determined. Odamex's spread and damage match that of vanilla Doom.
While I'm not that well versed on Zandronum or ZDoom 2.x's physics code, I probably qualify as an expert on the ZDoom 1.23b33 code as I added the ZDoom physics code on top of Odamex's vanilla physics code. Some of the general changes all versions of ZDoom have when compared to vanilla is wallrunning in both north and south directions, aircontrol, proper three-dimensional explosion damage/thrust, altered gravity, smoothing of the player's view when going over bumpy terrain, and non-projectile actors moving over/under each other.
Typically when you hear competitive players complaining about Zandronum physics, keep in mind that they are typically complaining about the differences between Zandronum/Zdoom 2.x physics and the ZDoom 1.23b33 physics that they prefer, rather than comparing it to vanilla. There appear to be some real differences that do change the feel of the game but I'm sure someone more versed in ZDoom 2.x would be able to offer a better comparison in that direction.
Last edited by Dr. Sean on 06-11-13 at 03:14