They use the same cores, so all other things being equal, they would perform the same. However, Intel's naming nomenclature leaves a lot to be desired when comparing desktop to mobile CPUs. Looking at Haswell CPUs:
Desktop i3 = 2 cores, 3-4 MB cache, hyperthreading, no turbo boost
Desktop i5 = 4 cores (mostly), 6 MB cache, no hyperthreading, turbo boost
Desktop i7 = 4 cores, 8 MB cache, hyperthreading, turbo boost
Mobile i3 = 2 cores, 3 MB cache, hyperthreading, no turbo boost
Mobile i5 = 2 cores, 3 MB cache, hyperthreading, turbo boost
Mobile i7 = 2 cores/4 MB cache, or 4 cores/6-8 MB cache, hyperthreading, turbo boost
There are slight differences in features too, but the above are the major performance enhancements. The other thing you can't see in the above is that the desktop processors tend to be clocked higher (and have higher power consumption as a consequence).
The biggest loser in the lineup is the mobile i5. It's basically a mobile i3 with turbo boost. Nothing like its desktop brethren which is quad core and has twice the cache. I recommend people avoid the mobile i5 unless it's only like $10-$20 more than an equivalent i3, or it's one of the low power versions which can turbo boost an extra 1+ GHz.
The dual core mobile i7 at least improves on the cache size. And the quad core mobile i7 is a pretty good match for the desktop i7 (other than clock speed).
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