If I want to say "Thanks for your help", which sentence is correct and which one is more commonly used?
It seems that the first one is more uncommon but I'm not really sure.
In my opinion, 帮忙 and 帮助 are different.
You would say,
Imagine that you are going to prepare a meal in your house,to entertain your friends, but you have a lot of work(buying, washing, cutting, cooking...) to do , so you ask me for help. You would say,
Now, for your question, I think the 2nd sentence is more common, though the first one could be understood. I guess you would not say "Thanks for your doing me a favor" in English, would you?
You can also say other words to express this meaning,
Also, if you want to thank someone for helping you by supporting you somehow, you could use
but it is rather formal.
I think both uses are correct, depending on the context. The former might be more appropriate for work and labor (as in you help someone do something), while the latter might be more appropriate for support and assistance (as in you aid someone in doing something).