Well, here's a decent comparison:
DirectX® 10
Mostly, you're looking at some stuff to really enhance high-end gaming. From what I've seen in Bioshock and Crysis, the real difference is in water (if you pump the graphics, it can look amazing). Some will probably disagree. But, the thing is, no low end card is going to be able to cover a lot of that stuff anyway. As with DX9, there will be some residual effects for normal users. But, keep in mind, all of DX9.0c still isn't being taken advantage of.
But, as you suspect, DX10 requires hardware support. A DX9 card can't give the benefits of DX10. A DX10 card can't give the benefits of DX10.1. But, in most cases, you won't lose anything. Few pieces of software have gotten rid of DX9 support. You should be fine for a long time to come. Wait until DX10.1 cards get reasonably priced (there are a few out there from ATI HD 3xxx series, but still cost more than the 1650). You should be fine for quite awhile. And when you upgrade, at least you won't have spent too much on your previous card.