The WCF model is vastly more flexible, essentially - if you only use it to present a basic http model using basic-profile and xml, with proxy objects - it'll appear very similar.
A brief list of differences though:
- much better support for emerging standards (although WSE2 and WSE3 are available for asmx, it is all much simpler in WCF)
- MTOM inbuilt (and fixes a known bug that I remember finding in WSE3 with MTOM)
- much wider range of supported transports/protocols etc, and the behaviours are fully configurable/extensible; for example allowing you to use a custom serializer/protocol/transport/etc seemlessly, just by changing the config
- much richer configuration, both at config and runtime
- full support for inspectors and custom principals
- ability to share object-models if you want
- you can host it outside of a web-server; a console exe or service, for example