I had a long chat once with an IM after I had played the White side of the exchange against him and he trounced me.  He convinced me that White really needs to be careful not to reach a losing position in the opening.  Black's play is fairly straightforward.  However, I have beaten players 1800-2300elo with the Exchange. I think it was mostly because they were caught by surprise since I normally play the main line KID.

I agree with Topnotch that it is WHITE not Black who is fighting for equality as long as Black is careful.    Here's what Mikhail Tal said in "Life and Games" (game 40)  when Boris(?) Ivkov played it in 1961:   

1.d4 Nf6 2.c4 g6 3.Nc3 Bg7 4.e4 d6 5.Nf3 0-0 6.Be2 e5 7.de5

"A rather unpleasant surprise.  The exchange of queens is a cold shower on Black's aggressive  intentions.  Apart from this, two psychological factors  probably influenced the choice of such a continuation.  Firstly, practical experience in my match against Botvinnik showed that it was possible to reckon on success even with this modest plan, and secondly, a longish absence from tournament play made Ivkov cautious.

Objectively speaking, a premature exchange in the centre can create no problems for Black."

His notes to the game (Ivkov-Tal 1961) are still pretty much the ultimate word on the Exchange Variation.  Tal actually won the game by going into a R+P ending rather than his trademark spectacular tactics.

Like you I prefer to cut down on Black's counterplay in the KID. My favourites are the Makogonov, Samisch, Smyslov (4. Nf3, 5. Bg5), and sometimes Gligoric (7. Be3). All of which keep complications in manageble proportions. 

The Exchange KID is hopeless as a legitimate winning attempt against the Kings Indian.

Nevertheless with careful and precise play White should equalise.

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