Not the right comparison
I've had a Slingbox and currently run two HDHomerun boxes.
The Slingbox does not give you access to the raw MPEG2 stream. There is (or was when I had one) no way to bypass the Slingbox's re-encoding of video. Frankly the picture quality on a LAN was bloody awful and there is no way I believe any of the Slingbox hype about quality. What it does reasonably well is to re-encode the video for lower bandwidth connections.
The HDHomerun is a more accurate comparison as it simply takes the input audio/video stream and makes it available over TCP/IP without modifying the stream. I wouldn't imagine it'd be too hard to take that stream and re-encode it in real-time for mobile/whatever on any PC/Mac. Just the same as this Elgato device.
Our HDHomeruns work superbly mounted up in the loft. Sorted out our signal problems nicely. Four tuners is enough for the whole house and running cat5e network cable is a lot easier (bends etc) than running good quality coax. I only mention this as lots of people end up having to use amps at the "TV point" and the cable between the loft and the "TV point" is likely cheap junk from 30 years ago which is going to be hard to replace in some houses. Do think about summer heat in the loft though.