Here are some lessons I learned being, and using, Adversary Players.
These are all in my experience; I don't make any claims these are universally true or complete.
Being an adversary.
It can be a lot of fun doing this. You really get to make some decisions that affect a game you otherwise are only peripherally involved in. It's like being a player, without the worries about your guy skewing your decisions. Plus you get to drop in on a game where, thanks to be outside it and being friends with the GM, you have too much information to be a PC.
It can be a throwaway role. You can try things out you might not try otherwise, and treat your troops more like wargaming chits than as valuable and irreplaceable resources. This is especially helpful to the GM because the Evil Wizard isn't likely to treat his orcs any better than that.
Having an Adversary
They'll do stuff you never do. As a GM and a player, you'll have tendencies to do certain things. You'll have NPCs act in certain fashions, prefer certain outcomes, and react in certain ways. Some you just won't do. But an Adversary Player just might. The example I gave last time of the A.P. having the PC's boss reward them for backstabbing the ally he sent them to aid is a great example of this. I'd never have done that - it didn't even occur to me anyone would do that. But he did . . . and that's one of the good things about having an adversary.
Their decisions, no matter how unfair, seem more fair. If as the GM you give out unequal rewards, or unequal punishments, or make a decision that clearly favors some NPCs or the bad guys or whatever over the group, it can seem unfair. Even in a group of adult friends, it might seem like, "Okay, he didn't want me to do that" or "He's trying to reward her to bring up her weak PC" or other meta-game issues. But with an adversary, it always feels fair. That person is remote, operating on limited information, and is effectively neutral in any intra-group issues. So the decisions seem as far as a random die roll but are also more inherently interesting. There is no "What if I rolled a better reaction roll?" because it's that guy deciding how his NPC reacts without any dog in the fight, per se.
Some of the same benefits of having multiple player groups and multiple GMs. One aspect of very early sandbox games I wish I could get is players working together and facing off. They individually change the world and change it as a group. These changes bang off each other like billiard balls. It's also similar to having a second GM, but without the coordination issues ("Bob can't make it, so only one GM tonight" or "We can't play because Bob isn't here to help GM.") You get someone else stirring up the pot.
You also avoid the "one controlling personality" problem of a GM. You avoid the complications of a co-GM but benefit from it. You can veto or modify decisions of an Adversary, because you're in charge. But you get some of the benefits of having another person with some behind-the-screen insight (yet not all of it).
There are a few things to keep in mind:
Don't pretend they are party members. Or fellow PCs. If an adversary player is playing an NPC, make it clear this person is running an NPC for you, either in person or remotely. Nobody likes a ringer; if you present a face-to-face adversary player as another player with just another PC and it turns out he's running a secret bad guy, bad feelings can result.
People might groan if their friend shows up to guest star at a game by running the orc army against them, but they won't be annoyed by it. It's not bait-and-switch.
It seems to work better with not-too-major NPCs. In other words, the players run the protagonists, you run the antagonists. The Adversary Player runs an important but not game-breaking character. I've had them run the PC's patron, a wizard's former master (that'd he'd turn to for advice), and a potential background NPC ally or indirect foe. I ran the major bad guys and immediate threats, but I'd get advice on the movers-and-shakers who weren't on that direct line of conflict between the PCs and the Big Bad. In a plot-based game, this means don't hand someone the Big Bad to run. In a "pure" sandbox, this means don't give out those NPCs the PCs are likely to come into direct and enduring conflict with. It takes too much of the campaign direction out of your hands, IMO.
Ask for If/Then Advice. The best way I found to use the A.P. was to ask for advice on how their NPC would react. "If they win this battle, what does he do? If they lose, then what?" Have some reaction options on the table, so you're ready to pull out the reaction when the PCs do one of those things. You can have some general reactions, too - what if they ask for aid, what if they ask for money, what if they fail a mission, what if they get busted by the law, etc. These if/then discussions will help you improvise when the A.P. isn't available in a timely fashion.
Only give the A.P. the appropriate knowledge. Some GMs have, or at least claim to have, a nearly mystical ability to firewall their GM knowledge from the NPC's available knowledge. I try, but I'm sure I don't. I find it's more fun to just not know and make decisions based on that. So I'd only give my A.P.s the knowledge they really had. "Here is what the PCs told you, and what your spies told you, and what you knew before. What do you do?" I leave out the stuff they don't know and get a more "genuine" reaction. Part of the idea of outsourcing your NPC actions is to have them only using a more appropriate and limited set of information. Don't spoil it by telling them everything.
It's a negotiation, but it's your decision. If the A.P. suggests something you don't like, you don't have to run with it. You are the GM. But it's worth trying to find something you both agree would be interesting and fit your mutual vision of the NPC's personality and role. Don't ask for advice on an NPC and then ignore it, but remember you need to chisel it into exact shape to fit your campaign.
Those are some of the things I learned from running the NPCs and from a much larger pool of experience having my friends run NPCs for me remotely.