Thanks to the wonders of DNA testing, and chromosome evaluation, it has been proven that the coastal brown and the interior grizzly are indeed the same species. Diet, amount of calories burned to capture meals, longer hibernation periods, etc. are all factors in why grizzlies are smaller than brownies.
I would also guess that evolution has played a part. Since coastal bears are concentrated in smaller areas, the larger, stronger ones would be more successful in fighting for breeding rights, and also for laying claim to the best forage areas.
In mountainous areas, smaller bears would have the advantage, due to fewer calories required for sustanance, the ability to cover more area in search of food, and greater efficiency in retaining body heat.
As for "biggest", polar bears or brownies, the largest measured brown bear is larger than the largest measured polar bear, but I believe that on average, polar bears are larger than brown bears.
It is also interesting to note that most bears are never weighed, and their weights are generally greatly exaggerated. Bear researchers over the last twenty years have proven to be thorns in outfitters' sides when it comes time to estimate a bear's weight for a client. According to a friend of mine who works for the Canadian government, and studies bears, the average adult male Canadian grizzly weighs in at around 450 lbs. Those over 550 lbs are EXTREMELY rare, but hunters and guides routinely report killing 600+ lbs grizzlies.
Whatever their actual weights, these are truly magnificent, awe inspiring animals. Any grizzly, to me, is a big one.