Um, that wasn't the plot of "The Great Escape." It sounds like an awesomely entertaining movie though. Are you maybe thinking of "The Sand Pebbles." I don't remember much about that movie, and I think it takes place earlier than WWII, but it does have steve Mcqeen, and it takes place in Asia.
More movies like this one?: Of course the one with Claudette Colbert. Also "Bridge on the River Kwi" and also with Claudette Colbert, "So Proudly We Hail." The last one isn't about concentration camps per-say. But it has similar storylines involving a group of women in WWII facing adversity. It's about a Corp of Nurses in the Pacific, but there's lots of action, suspense, and drama.
"To End All Wars" also deals with Japanese POW camp. It is a Scottish/English camp, but there is a token American, played by Canadian Keifer Sutherland.
"The Great Raid" deals with a mission to liberate a POW camp in the Phillipines in the last days of WWII.
"Merry Christmas, Mr. Lawrence" is another. Features David Bowie.