There's a post on this already......myself and others did a pretty exhaustive comparison of the differences. Do a search in this forum.....too lazy to find it now.
Alot more than just the turbo. Differences centre around internals/block/cams/turbo/fuel (obviously).......
But those differences have their main impact on a stock vs. stock engine.
Once mods come into play, both the WRX and STi engines have shown to be modified (both on stock internals) to similar (and serious!) hp numbers. So how far you wanna go....depends on how deep your pocket is
e.g.
A WRX engine with a STi TMIC, STi Downpipe (stock STi 2.5" w/ dual cats) and STi turbo w/ injectors (bigger injectors necessary for bigger turbo), can net close to 240-250 whp on a basic level tune, which is right in STi territory (or almost identical - on the same fuel). No internals/cams change. See my point?
<waits for others to chime on the "supposed" limitations of WRX internals

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