I know that the transmission and rear differential must have same gear ratio to work properly.  Car in question is an 08 Impreza WRX with 5MT.  According to cars101.com this was supplied with a 3.90 gear ratio.  Current ebay sellers are offering JDM transmissions with matching 4.44 rear differential.

Question is what would be the difference in operation if the MT/Rear Diff with a 3.90 was replaced with a MT/Rear Diff with a 4.44 ratio?

It would accelerate better off the line. Lower ultimate top speed...... that's about it. 

It's not a problem at all. Makes it a lot more fun or helps correct for larger tires. Lifted WRX's are something we do from time to time and personally I like the look. 

Thanks GD I knew you would know the answer!

Yeah in Japan many WRX were 4.44 ratio. The expressway speed limit is 100 km/h or basically 60 mph.

I'm OK with my 21 year old kid only doing 60 mph!