Less speed and range, OK. But a more modern radar (OK, so they could have upgraded that instead of making the AMRAAM), and more agile (more likely to hit those things that are in range). Phoenix was mostly for not very manueverable targets.
The smaller size and cost are advantages too, having more weapons and being able to carry more of them at the same time is useful.
Finally, if the need for a long-range missile does arise in the next few years, the US has European allies working on such a missile (Meteor, with a ramjet engine that is supposed to give it high speed (Mach 4) and full manueverability during most of its flight), and it's planned to be mostly compatible with AMRAAM, with modifications to fit it in the F-35. Not ready yet, but they're making progress.
http://www.janes.com/aerospace/milit...0515_1_n.shtml Raytheon had an AMRAAM variant proposal too (FMRAAM).