This is a familiar question for keyboard players; our instruments are stereo by default[note], so we have to decide whether to run in stereo or mono all the time.
The biggest issue with stereo is that speakers aren't very good at creating a uniform stereo image. There will be a sweet spot, where you can hear both parts perfectly. Outside of that spot, you'll won't get balance, or, in the worst case scenario, you'll get phase cancellation. Which will make you sound like garbage.
Stereo sound is undeniably better when you're listening through a nice pair of headphones, or monitors. My keyboard has far more nuance and detail in stereo. But the limitations of live sound make stereo a non-starter in most situations.
I would talk to your sound guy, but don't be surprised if he'd prefer to run you in mono. In the majority of situations I've seen, it's the best way to give the majority of the audience good sound. If he's not running the keys in stereo (assuming you have them), I doubt he'd want to run the guitar in stereo. I could be very wrong.
I've included some links to relevant discussions below. They discuss the pros and cons, and my general conclusion is that the extra complexity is not worth it.
[Note]: Todd rightly points out in the comments that there are quite a few classic keyboards that only have mono outputs. Stereo by default is a weak generalisation, but it doesn't really affect the answer.