I use both and both solutions work well. I prefer a reducer headset, though. The extra room gives the designers the ability to use larger bearings to take the load and the leeway to design a headset with almost no stack height.

Headset reducers are fine, though, especially if you already have the 1 1/8" headset on hand and wish to make use of it. The reducers insert as far as a deep-insertion headset, usually, so there is no danger of ovalizing a headtube just because you run an adapter. And if you want a bit of extra insurance, you can press a deep-insertion headset into the reducer.

If you want a super-beefy reducer heaset, check out the Syncros FBI. Yeah, it's a bit heavier than most; but that's a real Timken tapered roller bearing in the bottom end of that sucker.