We've been to Zermatt and Lech in the past two years ... both were fabulous, but Zermatt was more fabulous.
Now, the reasons for that aren't necessarily going to be the same for everyone ... they had to do with weather and other things that are variable. I think the two places were pretty similar. I was just more comfortable in Switzerland, for whatever reason. I'd been to both places before, although not to ski.
Caveat: the word "budget" wasn't terribly prominent in the picture. We ate like kings, had guides all day every day, and basically (this past trip, to Lech) tried not to do too many mental conversions from euros to dollars. We saved money here and there (like bringing our own skis, but that was more because I wanted to ski my own skis), but we treated the experience differently than we do on our regular ski trips in the US.
One more thing -- we always rent cars instead of taking trains ... I just like the flexibility of being able to go wherever on a whim. And it's really easy to drive over there. Well, usually. We made a mess of Zurich's old town on the first day.
(The GPS we had in Austria was great, though! Get one if you drive.) I like "getting lost" in strange places. You can do it walking, too, but it's fun to take side streets and country roads in Europe and see what's there.