You should actually be able to use either extension -- both can be mapped to your own custom IHttpHandler.
If I had to pick one to use, I'd probably go with a .ashx extension. One reason for this is that there are no built-in .ashx end-points in ASP.NET -- whereas there are a few .axd ones (for example: the new webresources.axd). So going with a .ashx reduces the chance of a naming conflict.
.ashx files also now have intellisense support in VS 2005 -- so that makes building them easier as well.
Hope this helps,
Scott