The buddy system is really neat, but suffers fatal flaws unfortunately. Instead of giving each buddy a unique advantage, they mostly crossover or multi-task to the point it makes another one useless.
My rankings.
1. D-Dog: By far the best buddy in the game. D-Dog can sniff out enemy targets at a range that is an unfair advantage to the enemy... he is also largely ignored by enemy soldiers unless they tell him to shoo. D-Dog comes with a lethal knife getup and stun getup... telling him to attack will allow him to jump an enemy and either slit their throat or stun them. You can do this while hiding in cardboard boxes. He can also draw aggro a close range by biting enemies. His enemy spotting is what makes him better than any other buddy, as he spots reinforcements, vehicles, weapons, and finds harvesting materials.
2. Quiet: Quiet is a lethal sniper buddy. She can spot like D-Dog but not as effectively, and only on command. Just roaming with Quiet, she only spots enemies she has her scope on and once she moves to a new target the previous target is no longer marked. You can command her to scout bases up ahead, and she will permanently spot the majority of targets, but not all of them at times if the base is large. She also wont spot reinforcements like D-Dog can. Plus, telling her to scout ahead leaves you blind to near by enemies until you reach the destination she is scouting. She can draw aggro off you better than D-Dog by sniping loud, or she can take out targets once you develop suppressed weapons for her. Her AI has some flaws however, as she can be too aggressive when equipped with lethal weapons. I've found myself trying to knock out a high graded target only to have her pop his head off in the process. If I am not on a mission I keep the tranq rifle on her.
3. D-Walker: D-Walker does a bit of everything... unlike D-Dog and Quiet, you can ride D-Walker for fast transit to locations.... it has a walk mode and a fast mode where it uses wheels implanted on its legs. D-Walker is unmatched for missions that you intend to go loud on. You can develop a heavily armored body along with an array of weaponry from gatling guns and flame throwers, to lock on rockets. D-Walker also has a very limited enemy spotting ability that you can command him to do when you are not on him. It's severely lacking and mostly useless. When not using D-Walker or D-Horse, you generally deploy a vehicle you stole... the advantage of buddies you an ride on however is that you can call them too you rather than having to run back to your parked vehicle.
4. D-Horse: Poor D-Horse. He is the first buddy you have access too.... he can't spot and he can't kill... The only advantage he has over D-Walker is that muddy/poor terrain doesn't slow him down. He is the most mobile and fastest way on any surface. Sadly this advantage is useless compared to the benefits of the other buddies. The only other minor advantage D-Horse could be considered to have is that when you are getting away with a hostage/prisoner/VIP, you put them on the back of D-Horse behind you, while D-Walker holds them out front for the shooting gallery.