Not really. All you've really missed is 2 new races which, for me, weren't great. The campaigns were quite enjoyable, and I suppose worth the money but multiplayer is where it's at and I've never played the two new races online as the vanilla ones are the best.
With vanilla CoH you can play against or with all the new races, just not as them. You still get to play the same maps as everyone else. You are only restricted as what race you play as.
Gizmo is talking about the new expansion; Tales of Valor. The campaign focuses on three tales of, well, valour. You can play on the Falaise pocket and two others. It's geared kind of like DoW2's campaign is. Rather than get a full army, you get one squad and as they level up they get more abilities like new weapons, run faster and so forth.
Multiplayer wise, you'll be missing out on quite a bit if you don't get it. If you get ToV it allows you to play as
all the races. Brit, American, PE or Wehrmacht. You also get to switch some units for others. If you look at the image Gizzums linked you'll see that these units replace others. As far as I'm aware these aren't just aesthetic. The purpose of the replacing unit is essentially the same, it just does it a little differently.
All in all, new units, new maps, new game modes and new campaigns. Sounds great, but forgive me if I'm a little pessimistic after the patch to fix all patches was released last week (actually due for last November) seems to have caused quite a bit of harm. I'm not all that optimistic about Relic anymore.