JayMan said:
finasteride if you have minor hair loss and want to maintain
dutasteride if you want to regrow, or you stopped responding to finasteride. or if you just want the most powerful oral drug out there for hair loss.
I'd say always finasteride first, since it's approved for hairloss and dutasteride. isnt.
Also, it's not as strong, doesn't affect the 5AR in the brain, and works very well for most people. it's not for "minor" hairloss only.
Also, your doctor is less likely to prescribe dutasteride. for hairloss, (probably not likely to do it at all, unless you've tried finasteride. first and it didn't work) so people are more likely to use it without the supervision of a doctor.