2 Bishops versus Rook

This position is a little bit simplified from something I ran into with the computer.  Technically material is even but is it really?  What should the strategic thinking be for each side?

Your strategy should be to break open the queenside with your connected pawns while holding Black's passed pawn back.

I am kind of wondering about the rook though.  It seems like black needs to get on the other side of the pawn to ake threats, if he just advances the bishops can trap him.  If it was black's turn he could probably play Rh1.  On white's move does it make sense to play Be4/f3 and then then a4 or just start pushing the pawns to open up the king?

My instinct about this position is that it's all about the passed pawns.  If the black h-pawn gets too close to promotion, white may be forced to sacrifice a bishop for it. The same is true the other way around, if the white f-pawn gets too far up the board, black will have to sacrifice the rook to stop promotion.

If the black rook were behind the pawn, white could blockade the pawn by setting a bishop in front of it. The black rook has to get out from in front of the pawn eventually, but he can't do that if the pawn is attacked.

I think I prefer white in this position even though the black pawn is further advanced. I think the bishops can keep black from making too much progress there and white will be able to push the f-pawn.

I haven't looked at any specific variations.

I'd say white has very little chance to lose. After Be4!, it seems like black really can't push his pawn forward (or he will get his rook trapped), or get his rook out of the way (or he will lose the pawn/allow white to activate king/allow a f-pawn push)

In this position, I would say the 2 bishops are definitely better than the h-pawn and rook, because after Be4 they seem to completely restrict them while still controlling other parts of the board. 

I agree Be4 looks good and if Bh4 then Bf3

Without tablebases that cover this many men or a skilled GM to help us, doubt we can know for sure. 

My iphone shredder, given time to think to a depth of 21 moves, recommends 1. Be4 and gives the position an evaluation of +1.47.  Be4 certainly looks like a highly reasonable move, in that it improves the position of the bishop somewhat, while preventing blacks king from moving towards the action, and restricting black's rook's options.

If 1. . . . h4?!
   2. kb3!  and shredder likes the position at +2.03 at a depth of 23 moves, apparently because the black rook's freedom of movement is so badly restricted that white has time to get the king into it.  Seems reasonable.

1 . . . Rh5 is apparently a much better defensive try, after which shredder choses to stay on the diagonal with 2.  bf6, rating it at only +1.30 at a depth of 21.  Shredder doesnt much like any of what look like black's natural plans to me.  If black tries to get out of the way of the pawn with rb5, shredder likes 2. bf3 at +1.50, forcing the rook to go back, and proving time for ka2 to b3.  If Kb8 (to try to bring it into the action) then 2.  be3 attacking the rook followed by 3. f4 is +2.21 -- cant say as I'm real clear why this variation is so much worse for black.  So what shredder likes is the seemingly odd pawn move 2...a5.   

My idea for white, 1 bf5, shredder does not like nearly as much, after black plays 1 . . . rh1, rating it only +.91.  Perhaps because black now has more flexibility with the rook.   

None of which proves anything really...except that this is a complex ending.