Design a Turing Machine which accepts strings $x \# y$ where $x \ge y$
zigzag left most side and compare each input to compare the 1's with each other. 


That is the right idea -- comparing the input one character at a time will work.

However we should be careful that we are comparing the right digits. For example, we don't want to say that 11 is bigger than 101 just because we compared the first two digits only, and said that 11 is bigger than 10. So, maybe it would be helpful to have, as a first step, to see which of them has more digits. Make sure that you ignore leading zeros when doing this.


  but i think i'm way off


Not at all, you have the right idea.