If me, I will go to the big name doctor if they cost roughly same.

You can use question tips from OCV site:
http://www.oneclearvision.org/treatment-for-eye-floaters/questions-for-your-doctor/

But the most important question is a question to yourself:
Are you ready to give up your eye vision?

Yes, there is no guarantee you can't have complication even in the hand of great doctor. When you decide to do the FOV, just consider your eye is done. Don't expect too high, be prepared for worst things, plan what will you do next if the result is not what you expect. Give some thoughts to every aspect of your life (job, spouse, family, dream, hobby, etc). Tell about this to your family or close friends too so they are not surpised when things doesn't come as expected, hopefully they will always support you and make you strong.