I think if done well, symmetry can look great. At times though runs the risk of looking too perfect or planned out, which isn't necessarily my favorite. Rich Hardy posted a black and grey front on Instagram recently that I think does this very well.
I have some spots where similar ideas and similar sized pieces play with one across the body, but aren't exactly symmetrical. For example, a very straightforward tudor rose on one knee, then a weird rose morph on the other. And a darker death's head moth on one thigh and a butterfly on the other.
Ultimately, your call to go with what you think looks best!