So I think the answer to this question would be an obvious one here, obviously the 1080ti...

I think your question should also factor in the cost to performance ratio of the 1080 and the 1080ti.
You are going to spend around $200-$300 more for a 1080ti.
If you have a look below at the calculations from nicehash on both cards.

Please see the 1080 below:
https://www.nicehash.com/profitability-calculator/nvidia-gtx-1080?e=0.1¤cy=USD

and the 1080TI below:
https://www.nicehash.com/profitability-calculator/nvidia-gtx-1080-ti?e=0.1¤cy=USD

So the income per month right now on the 1080 is $151.77 and $176.13 on the 1080ti.
That is a difference of $24.36 per month that you would be earning extra.
So to make up for the income difference per month is going to take some time.

Just take note that the 1080ti also has a higher power consumption.