I've been learning English for many years
This is present perfect which says you started learning English sometime in the past and you are still in the process of learning.
I've learned English for many years
This is in present perfect and it's not quite correct I guess, cause the verb 'learn' here would imply that you have learned just about everything. learning is a continuous never ending process. You could rather say I have studied English for many years, which would sound just fine.