I own the Digital Stream, but can tell you the Humax offers these main benefits over it:
1. Network streaming functionality i.e. you'll be able to stream programs on a DLNA enabled PC / NAS and watch them on the Humax.
2. The Internet TV portal services which are coming online soon including iPlayer, Sky Player and YouTube (though the DS will have iPlayer as soon as the BBC start the MHEG broadcast sometime soon).
3. Being able to auto-pad recordings i.e. to set a few minutes either side to absolutely be 100% you'll get the whole recording. Both the DS and the Humax use a system known as Accurate Recording which relies on the Now/Next information provided by the broadcaster. So far, I've only had one recording on the DS where the end was missed in 5 months of ownership. However, some broadcasters can be poor at doing this (Channel 5, I'm looking at you) so the Humax offers a bit of protection from that.
4. Ability to record the buffer i.e. if you've been watching a programme and then decide you'd like to keep it, you can rewind to the beginning and then set it to record. You can't currently do this on the Digital Stream (though it's on the wish list to be implemented).
On the other hand, the Digital Stream is £100 cheaper and also offers a Picture in Picture mode that the Humax doesn't i.e. the ability to watch a channel or a recording and have a small screen in the top right hand corner showing another live channel.
Hopefully this will make things easier to decide between the two - you can also read my fairly thorough review on the Digital Stream
here.