Here is a good link describing some of the differences: http://hodgdon.com/tripleseven.html

Here are a few of my personal observations:

Ignition: Pyrodex is easier to get to fire in a sidelock. If you are talking #11 primers, all are not created equal. If I am using 777, I always us CCI magnum primers or musket caps. Musket caps are a LOT more powerful. With 209 primers, pretty much anything will make it go bang, but the weaker primers (ex: 777 primers) will result in less "crud ring" so a lot of people shooting 777 use them.

Accuracy: In my guns, pyrodex has been slightly easier to find an accurate load. Although I have heard people say the opposite, I think most people give a slight accuracy nod to pyrodex. I have always been able to find an accurate load with 777, but it usually takes more experimentation.

Power/velocity: In loose form, 777 is 15% more powerful than pyrodex. Pellets though are made to be equal unless you use the 777 magnum pellets.

I believe that 777 has the sulfur taken out. Less smell and slightly less corrosive. I don't worry so much if I can't clean a gun shot with 777 until the next day.

Crud ring: Although 777 has had more bad press about a "crud ring", I find that both of them make one where the powder/bullet sits, making it harder to load subsequent shots without swabbing.

Cleanup: I give a slight edge to 777 in that it really does clean up well with just water. However, anytime you use water to clean a firearm, you need to finish by pouring boiling water through the barrel so the hot water will evaportate quickly, then run dry patches and something for corrosion protection through the barrel (remoil etc).