Unfortunately its going to be really hard to have a build that will work well for both PvP and PvE, after your done running through Inferno and have had time to stock up on the runestones you would need you could easily level another DH to 60 and then gear with stuff from your PvE DH for PvP.
So, to the build. Good try.
First fundamentals will most likely be removed from the game before release. Recent blue posts hint at this quite heavily as there are almost always better ways to get your regen. But going with the just in case scenario I didn't alter it as your generator.
This is the PvE build for you:http://us.battle.net/d3/en/calculator/demon-hunter#bYUlQk!YdU!YacbYZ
I'm assuming that you would only use evasive fire for the distance creator, that's a little iffy for this build, could accomplish the same thing with vault, but evasive is cheaper discipline wise and the same distance so I agree with it for your build, but if you found that you were using it a lot you would need to get rid of fundamentals, and probably steady shot.
Steady shot I left in there, but I really doubt you'll get much use out of it past NM.
On the other hand you don't really have much discipline costs at all, so preparation was ab it of a waste. Shadow Power will be used for bosses and champions mostly, and you needed more power in the build, so I replaced elemental arrow with RoV, its crazy powerful now, and gives you a bit more utility as well. Prep and Vengeance will give you the hatred you need to use it more often. Perfectionist is in there to allow you to use Prep and Shadow Power in tandem if set up right with a few health globes to get the last few discipline you would need. I would also consider Crimson on Caltrops. Vengeance is mostly for the increase in hatred, but if you save your health globes and create a kiting pattern that allows for you to pick them up when you wish it can be a good storage bank for emergency resource regen or health regen. You would never be at full hatred to get anything out of Hot pursuit, not enough regen, and too much of spenders.
For PvP, you need to get rid of Fundamentals. This is what I would use sticking to your build as much as possible:http://us.battle.net/d3/en/calculator/demon-hunter#bYgZQi!aZf!YcbYac
It's really not much like your original build. Remember that it will be 3v3, I'm going to assume you haven't done arena's in WoW at least since stun lock went out the window, if you have my bad, hard to tell without a WoW icon. It's all about CC chain on on or two targets and then bursting one target down.
You don't want the extra distance on evasive, because you'll be on the outer edge of the arena a great deal, taking advantage of LoS, but it will still be useful for hoping gaps in the floor when you can't help but get drawn in.
Mark is your healing ability now (and will most likely heal anyone who is attacking that target as well.)
Smoke screen is pretty much mandatory in PvP the ability to turn invisible is priceless.
FoK and Caltrops are your slow. Impale is your single target burn move. I would have rather gone with with Rapid fire or Strafe, but it sounded like you didn't want anything channeled, and if you used strafe it would require dropping mark most likely, which leaves you without healing. And rapid fire would require Prep, and you just simply don't have room.
I would have actually changed quite a bit more but wanted to leave some of it intact. The passives are all pretty self explanatory.