Advice on Pos battery cable terminal.

Ok i just replaced my cable, however i have a question, the previous cable on the positive side that goes to the fuse box was as thick as the battery cable itself, however now on the new one i got the wire going from pos battery terminal to fuse box is 2 or 3 times smaller than the battery cable, is this ok or should i continue to use the original one because it is so thick.
I guess i am not understanding if the same amount of juice can pass thru the small wire as well as the big wire safely.

Thanks for the info.