If you read the Subaru boards, most STI owners admit that the EVO has a slight over all performance advantage from the factory in terms of handling and acceleration.
Comparing an EVO to an STI is like compairing an RSX to a GTS. The RSX technically has a slight advantage, but when it comes down to it, it's really going to be a drivers race.
I personally like the looks of the EVO better than the STI.
I personally like the boxer engine that the STI has better than the traditional engine in the EVO.
For what it's worth, I drive a 1991 Subaru Imprezza wagon as a winter beater and it has over 250,000 miles on it and it still runs like a champ. In fact, I still average 25mpg from the engine, and it doesn't leak/burn any oil/fluids. Mitsubishi's in general tend to be a little more problematic when you modify them for more power. It's not to the point where they would be considered unreliable, but you just seem to have more problems with a souped up Eclipse or 3000GT for example, than you would with a souped up Honda/Toyota/Nissan. So I would say that Subaru probably has a slightly more reliable engine, but Subarus are known for having weak transmissions, so it has the disadvantage there.
Basically, each car has little advantages and disadvantages, but over all, the two cars are pretty much equal IMO.