Different beasts. A direct comparison is unfair to either of them.
Uglify does minification and dead code removal. That's really it.
Closure does a lot of type checking, code rewriting, and has a very specific subset of JS that you'll have to use if you really want to get the best performance out of it... and does minification and dead code removal.
If you just want minification/dead code removal then Uglify is waaay faster, javascript native, and almost as small (105-120% of the size of Closure compressed code, depending on the code). It also doesn't use the JVM so that can make dep management/ops simpler if you don't already have java in your stack. YMMV.
If the advanced stuff sounds like something you'd want/need (if you have a large project and don't mind writing to the Closure optimizations) then Closure is certainly worth looking at. It's very good at what it does.
Beats the pants of it - if you can live with the limitations.
It doesn't change string access, but it does rewrite dot access so you have to use dot access except when dealing with e.g json.
It doesn't work with the with statement, or code that is run with eval. You have to specifically export functions that should be used outside the code, otherwise they may be inlined, renamed or deleted.
Finally to get the most out of it, you have to write jsdocs for its types (at which point it can now do things like inlining functions).
Uglify does minification and dead code removal. That's really it.
Closure does a lot of type checking, code rewriting, and has a very specific subset of JS that you'll have to use if you really want to get the best performance out of it... and does minification and dead code removal.
If you just want minification/dead code removal then Uglify is waaay faster, javascript native, and almost as small (105-120% of the size of Closure compressed code, depending on the code). It also doesn't use the JVM so that can make dep management/ops simpler if you don't already have java in your stack. YMMV.
If the advanced stuff sounds like something you'd want/need (if you have a large project and don't mind writing to the Closure optimizations) then Closure is certainly worth looking at. It's very good at what it does.
Choose the right tool for the job and all that.