The spec of the Belkin HD is pretty nebulous.
It talks about 'High Definition' and 'near CD quality' etc but there is no mention of AptX. Or anything else specific come to think of it. In fact there is no indication as to exactly how or why it is HD and the old model isn't. So I'd have to say 'no aptx' although my Sennheisser BTD 500 USB BT transmitter does do aptx but doesn't actually say so on the tin. So who knows for sure? If you find out please let us know.
I don't ever use it for critical listening. To be honest I expected it it be crap and was delighted to discover it wasn't. In fact it's very good. More than good enough for the job anyway, Which is usually letting mates connect their 'phones easily and quickly to the big system. Also for when feeling particularly lazy and lying on the couch flipping through my collection on the netbook.
I also have one of the original non HD versions. With that one I'd formed the, totally speculative, impression it worked better with mp3 than with losslesss. As if the input was already efficiently compressed if didn't have to do so much work and risk getting it wrong. However, you know how easy it is with audio to make things up and then find your ears agree with your expectations? The new one seems the same with lossy or lossless. So far anyway.
I previously posted my experience with inexpensive BT gear here. Post # 7.