777 makes less smoke. It is stronger than Goex by volume, altho they seem to have calmed it down some since it was introduced. In guns that do well with it, it can be a good powder. It is about as hard to ignite as Pyrodex. On a dry day the fouling is hard and gritty. If a shower happens and it gets humid, that fouling will literally turn into a mushy runny mess. The powder is not too bad about moisture but the fouling is worse than black or Pyrodex about drawing moisture. When it is dry, a hard crusty ring happens in the barrel right infront of where you would normally seat the ball. It requires a damp patch to properly seat the ball at times. If you don't use one, you will be seating on fouling and not on the powder. This is easily verified by ramrod mark. Modern shallow rifling guns suffer this worse and faster than the deeper roundball rifled barrels. It can be very consistant in velocity in the smaller calibers. 3f is hot stuff, so start low. On a trip to the lake squirrel hunting, the gun worked fine to start but became crankier as the day went on. The powder is less corrosive, but if it keeps the barrel wet all the time, the result is the same. Cost, power, ease of use, and everything else makes this a workable choice, but it comes in dead last out of the three choices.
Pyrodex is the most corrosive. It is hard to clean your guns well enough to prevent it from damaging them over time. It has a higher ignition temp. I have been shooting it for years, and some folks laugh at how I load my guns. 20years of Pyrodex will do that to you. Be warned that the various lubes react differently with the various powders. It takes more than just changing powder to make a new load for a rifle with any of them. Pyrodex stinks bad. It draws the least moisture to the fouling of the three in the same situation. If something like bore butter is used, it will often not be a problem at all in damp weather. I remove the screw and put a 2 grain prime under the nipple when hunting to make sure it goes off. It is the least attractive of the choices, but it is the same price as real black pretty much. Since it is lighter than black, you get a few more shots per pound. Pyrodex is capable of very fine accuracy with P being the most accurate powder I have ever used over a bunch of time and guns. That isn't really fair tho, since I used little else for 20 some years. It is a workable choice that requires powder specific methods. It is second place to me.
Real black is easier to ignite. It produces easier to manage fouling in most guns than either of the others. There is more of the fouling but it is softer and less of a pain. It is not that bad about drawing moisture, but the fouling draws moisture like a sponge. It has the most choices in powder levels going from Graf's to Swiss according to the latest info posted here. It is more accepted in the ML'ing community. It is traditional. It works easier doing the same job the others do. It is also a different class of explosive than the first two. It is being regulated and insuranced out of existance in many places. My closest source that I know of is a 2 hour bumper to bumper round trip that costs enough that a pound of black costs me more than 777 would if I just bought a can up the street. If I could get black nearby one pound at a time, I would shoot nothing else in any of my guns.
If you can still drive a few miles and buy a can, be thankfull. If you can, then shooting anything else in a sidelock gun is just beating yourself up for no reason, altho it is doable.
If you take the time to patch the gun out between shots, use a prime like I do when hunting and the gun will be loaded for a long time, and you are shooting a cap gun, all three are workable choices with different pitfalls. The price of 777 is rediculous. Pyrodex is plain nasty to smell, clean, or shoot. I have killed a lot of game using it. Real black is the best and easiest to use, hands down, if you can get it.