I've tried Bikram and Ashtanga. IMHO Ashtanga is harder, but at the same time, easier to do, because you don't have to do all poses in one session. When I started Ashtanga, I only did Sun Salutations for almost 1.5 hours, followed by the cool down poses. You also progress at your own pace -- some of my classmates were doing headstands while I was still doing the basic poses, but that's not a problem. Each pose has an easier version, and when your teacher sees that you're ready, you're made to do the original version.
On the other hand, in Bikram, you're required to do all poses in one session. Some poses have an easier version, but for me, I prefer the gradual progression offered by Ashtanga.
I had one session of Bikram after months doing Ashtanga. I found Bikram more manageable than I expected it to be, partly because I already had Ashtanga training.
One note about Bikram: it depends on the instructor. My friend who introduced me to Bikram made sure that our Bikram teacher was the kindest one in the studio, and he also didn't make the room unbearably hot (apparently, it's the instructor who controls the thermostat).
They also have CARPET IN THEIR STUDIOS.
Not in the Bikram studio that I went to. They had hardwood floors.
For weight loss, Bikram's great. Flexibility wise, I think it is equal to Ashtanga. The nice thing about Ashtanga is that you don't need a hot studio for it, and therefore can do it at home, but some people prefer the environment of a hot studio.
Try both, if you can manage it.