I own all Panzer Campaign games, except Smolensk and Korsun.
The focus of Panzer Campaigns is tactical, while TOAW is operational, as you can tell by the title - duh!
This means Panzer Campaigns usually have more "realistic" rules regarding movement and combat. A couple of examples of those tactical subtilities in PzC:
-the biggest units in PzC are usually regiments, no brigades or divisions.
-units can move in two formation modes in PzC: Travel or Regular, depending on what you want them to do and at what speed.
-units can do direct fire (firing into an adjacent hex without advancing into it), assault (advancing by force into an adjacent hex), or do indirect fire for units with that capability.
-Logistics are more complex with concepts such as Virtual Supply Trucks or Explicit Supply.
-Control & Command is more developed. You can reattach units to different Corps HQ at night. Command radius of HQ varies depending on their quality and other factors. Command is also an important factor in supply.
-Opportunity fire is quite extensive
-Concepts such as Fatigue are dealt independently from supply, as it is in TOAW where you have a color rating telling you the general state of your unit.
So basically, all factors that can make a difference tactically are more developed in PzC since this is the focus of the game. In TOAW, these factors are meaningless since the focus is "higher up" somewhere between tactics and strategy.
Where PzC isn't as good as TOAW, it is definitely on the graphical interface, which is less nicer than TOAW and also on things such as Theater Options in TOAW.
As Maddog pointed out, it's true that it's quite bothering at first to see that there are no values on counters, as it is traditionnally the case with other games. But I must say you get use to it after a couple of hours. Still, the interface could use a facelift.
All in all, I can't say really which wargame I prefer between TOAW and Panzer Campaigns. They are both professional games for serious wargamers. If you already like one or the other, there is a very good chance you won't regret buying the other one.
For tactical realism and historical accuracy, PzC is the better game. But I like TOAW for the incredible variety of historical scenarios it offers, and for the better integration it does of operational and strategic factors.