Bikram yoga or Pilates

I did a few weeks of pilates to help with a back injury. I also did about 2 years of bikram. I found both good for improving flexibility although admittedly, I'm not as familiar with Pilates. Somebody might be able to provide a better comparison.

However, what I will say is that Bikram had a fantastic effect on improving my mood, diet and sleeping habits. I came out of each class feeling relaxed and stress free. I was starving but I wouldn't crave a massive helping of carbs or junk food. Strangely I craved healthy and light food after each class.
I slept like a log every night of the week if I did 2 or 3 bikram classes. I didn't feel this after Pilates.

I found Pilates was good for addressing the tightness issues I was having with a back injury. But Bikram was fantastic for elevating my mood and relieving stress. I'm not a spiritual person. Far from it in fact. I don't really buy into the whole using yoga to calm your soul etc. I don't meditate and tend to focus solely on the physical side of a yoga class. But the calmest and happiest I've ever been was during the 2 years of Bikram.

I can't answer your question specifically regarding flexibility or strength. But I can recommend the additional benefits which I found in Bikram. Also - it's a hell of a challenge in that heat!

Hope that helps