This is not a solution you can generally suggest because it rely on the toString() implementation of each object in the list. Also, this will create a lot of objects since you are creating each String (calling toString() on each element on the list) and combining all the Strings into a big String which are then compared with another big String. Therefore, the performance is scaling really bad when the lists are going to be big.
Another problem are you need to generate the full toString() String of each list before you can start the compare. So if the lists are not equal you have wasted a lot of memory just to find out the first element in each list are not equal.
And just because two objects gives the same toString() output that does not make them the same. And sometimes, two objects returning different toString() should be consider the same. A big problem is the standard toString() for all objects which just returns "Instance of 'TYPE'" so you solution can easily make some errors.
Please read the comment from Mattia which is consider much better.