The difference in your case would be very small. You can get a brighter picture on standard projection mainly because of the screen options (gain, etc...), but overall if you have complete light control for both rooms and you do proper calibrations it will look roughly identical from a pure quality perspective. There are other pros and cons of each. Shadows, ambient light, space, cost, and more. These should be higher on your list then quality. If you do a proper setup of either the quality will be basically equal.
Most home users do not have the option for full throw rear projection. They use mirror units and about 4 feet of wall space vs 10-16 feet depending on your screen size and projector. I have always found rear projection to offer benefits more in business uses. Where people might walk by the screen and you don't want them to shadow the image. Also you can have the lights brighter in your main viewing area if using rear projection since the source is in a controlled room behind.
