Streaming video to iOS devices is rather a special case as they don't support the RTSP protocol most commonly used for streaming video. Rather, they only support the Apple-invented HTTP Live Streaming. While I might be wrong as I'm yet to actually try it, the experience I have with MPEG4 and h.264 tells me that HTTP Live Streaming will be rather computationally intensive—you'll end-up encoding up to 4 h.264 streams for one stream, and h.264 takes more 'effort' to encode than MPEG2.
I've been looking at the same thing for my MythTV box, and the most promising thing I've found so far (though I'm yet to actually try it) is Carson McDonald's HTTP Live Video Stream Segmenter and Distributor.
I've also considered grabbing an Elgato turbo.264 as there are apparently linux drivers available.
Oh, and if you're in a country that uses h.264 for HD broadcast (like the US—I'm in Australia where we use MPEG2 for everything) you may not even need to transcode the video (at least for the high-bandwidth stream).