Is it appropriate to ask professors at which schools their recommendation letters have more power?
I would ask your references for "coaching help" with your letters and being strategic with who writes your letters to which schools. As part of the coaching, there are two questions I would ask:


"Do you (the letter writer) any connections to or experience with the programs I am applying to?". For example, did they attend a program? Do they collaborate with faculty in that program? Does your program regularly send students to a program? 
"What are you thoughts about the programs?" This allows you to make sure your reference is on good terms with the programs you are applying to. For example, if the graduate admission chair is feuding with you letter writer, this might be (unfairly) held against you.