I have a 3PH splitter. It has it's own PTO pump and is not dependent on tractor hydraulics, so it's MUCH faster. I believe it's also more powerful as it's a bigger pump.
Advantages: No extra engine to maintain. No tires to go flat. I can't prove it, but I'm pretty confident that it's more fuel efficient. With a 20 horse diesel running the pump, it's darn sure more powerful. With the 3PH, I can set it to whatever height is comfortable to work with. Or, lower it right to the ground to set a big round on it. Moving it to wherever is just a matter of hopping on the tractor.
Disadvantages: Initial price was fairly steep but not really bad for the power. It's a bit of a pain to put on and take off. It ties the tractor up when it's in use, but that just takes a little planning.
I usually have the splitter on the back and the forks and grapple on the front. With the tractor and a chainsaw, I have everything I need to turn tree length logs into firewood.
Works for me.