Hmm... Well, let's look at this. The 3800 is a pushrod V6. 2 valves per cylinder, no adjustable valve timing, and 90* requiring a balance shaft. The Mitsu's 3.8 (just guessing, but going off the norms for V6s these days) is probably DOHC (4 valves per cylinder), variable intake and exhaust valve timing, and is probably around 60* making it smoother, which is less power lost to vibrations. It may even have direct injection, but I'm not sure.
Then, take into account that in general the 3800 Series II is using 1996 technology, with a limited engine management system. Modern ECUs from all the manufacturers these days have ten times the processing power and around ten to twenty times the memory for storing more tables with more detailed values. The PCM for the 3800 Series II has 512kB of programmable memory to store calibration tables for the engine and transmission. The ECU for my boxer engine in the STI has 16MB available of programmable memory and only needs to control the engine. It makes 305HP (2 more than the 5.3L LS4 V8) out of a 2.5L turbo 4-cylinder boxer.
The 3800 in general is fighting about 14 years of progress since its last major refresh. It's a great engine that I will always love, just for its underdog-ness and reliability, but things change and you can't expect it to keep up with today's cutting edge technology.