The differences aren’t so much in the pieces as in the changes in gameplay.
The main difference in Panzer Corps is that units no longer need to move & attack in the same motion. One unit can attack, then another unit can attack, then the first unit can move. This is true even of artillery, and it makes the puzzle-piece frustrating movement of PG a thing of the past. Units cannot however, split their movement (i.e. move unit 1, move unit 2, move unit 1 again) — except for recon units, giving them a bit more usefulness.
Also, while units no longer get automatic elite reinforcements after a battle, they can be overstrengthed in between battles.
One other big change is ‘hero’ units that can gain special abilities. It gives the core units a little more personality (I’m not a big fan of it, though).
Upgrades are intended to be to newer versions of the same equipment — ‘cross-upgrades’ are more expensive.
There are also ‘dual-use’ units. This essentially is for the Flak 88s, which can spend a turn to convert from pure AA role to pure AT role, although a few other units exist. (And AA & Air Defense are combined into one type).
The units, and especially the scenarios, do differ from the original. Bridging engineers are no longer the king of infantry — now they are more specialized. The gameplay changes pretty much require different scenarios, and they are all redesigned.
To get some idea of the UI changes, you can play Panzer General Forever. PGF is an exact-as-can-be remake of Panzer/Allied General (and some experimental WWI games) for modern Windows (i.e. XP or later), with some considerable interface enhancements. It’s free, and the programmer was then tapped to work on Panzer Corps.