Sounds like you have the Sony A100 --- I had one too, and recently upgraded.
The Sony NEX will give you "dSLR" quality, as it uses the same APS-C sensor used in most Sony dSLRs. Your lenses would also continue to work, but with an adapter. And truthfully, that's useful when you have high-end glass you want to keep (thousands of dollars worth of lenses), so probably not that relevant for you.
The NEX system is a great camera. Definitely get dSLR quality, in a much smaller form. The main downside compared to a true dSLR, is the focus accuracy and speed doesn't quite match a dSLR. But it is pretty close.
The other option, in a similar price range, is the Sony RX100. Ultra high-end P&S.
It's image quality can come very very close to current dSLRs. In fact, as an owner of the RX100, I found that it's image quality surpassed the Sony A100. And it's image quality can match/surpass newer dSLRs when just using kit lenses.
The main downsides of the RX100 is limited telephoto reach (only about 100mm equivalent), and you don't quite get the background blur you can achieve with a true dSLR.
Comparing these 2 options, my main considerations would be:
-- Do you want to change lenses? If you want to change to the right lens for the right shot, then go with the NEX. (For example, I use about 7 different lenses for my dSLT camera). If you prefer the convenience of just having 1 high quality lens without the need to change it, then go with the RX100.
-- How important is "compact"? If you want a camera that is easy to carry 24/7, that can fit in your pocket, that you never need to leave at home... Go with the RX100. If you are still okay with a separate camera bag, just want to keep it smaller and lighter than a dSLR, then the NEX is a good choice.
Some other factors:
-- How important is low light? The NEX will perform better in low light IF you add a specialized lens. The RX100 will perform much better in low light just using the included lens.
-- Do you like intense portrait background blur? If so, the NEX is a better choice.
-- Do you like super sharp landscapes? If so, the RX100 can be the better choice.
-- Do you need a long telephoto? Particularly, shooting wildlife, birds etc? Then you would need a telephoto lens on the NEX. And the RX100 won't really give you that long reach.
Personally, I own both a Sony dSLT (the A55) for certain types of shooting. And I own the Sony RX100, as my "always with me" camera. In fact, my last trip to Disney, I used only the RX100. It was very freeing to be traveling so light, and I still got spectacular dSLR quality photos.