First of all, using Avermedia Live Gamer HD cards (both internal and portable) as a encoder for streaming material is pointless. Quality is rubbish. It's just a simple grabbing card with some kind of internal unit for encoding. But tell me, does it have the same power as i5/i7 CPU which can encode quite nice quality material? Nope. So using this type of card can make sense only when using it as a grabber/video source for encoding with such software as OBS. But as many people say it would still eat up some CPU power while grabbing too. So if you just want to capture game you play on your PC and encode and stream from that PC then buying Avermedia Live Gamer HD is... pointless again. It's better to add this money up for a better CPU. The only situation in which having Avermedia Live Gamer HD as a capture card is a good idea it's when you capture external source like console game (X360/PS3, any HDMI source) or secondary, gamer PC (PC with LGHD works as a encoding/streaming machine only then and you play the game on other machine which outputs it's video to LGHD). Then and only then buying Avermedia Live Gamer HD can make sense.
And one more thing. While many people say it's not possible, it is possible to both capture and encode material just with Avermedia Live Gamer HD. But you can do this only by using ReCentral - Avermedia software for Live Gamer cards. But it's just simple capturing of material without making and managing any scenes and stuff. And still it's pointless because internal Live Gamer HD encoder is a joke by design. And yes, XSplit can utilize internal LGHD encoder but again - quality is rubbish (especially in lower bitrates which are common in streaming).
OBS can only use LGHD as a video source (capture card) and - as I've mentioned before - it's not worthy if you plan to capture (play) local source and encode/stream from one PC. You can stay with OBS Game Capture / Window Capture methods. So get LGHD if you plan to capture console games, gaming source from secondary PC or if you play some really nasty game which you can't capture with OBS internal methods. And don't count on it as an encoder machine which will free up your CPU from hard encoding work. It's just too weak to handle decent encoding quality.