I guess what I would like to know is would I be fine with my Sigma on the 60D, would it match the image quality of my FF when it comes to landscape? Not only do I not have the budget for a new lens right now, but even when I do it would not be a super expensive L lens or at best the more affordable 17-40mm. But even then, my Sigma is equal to 13mm on the 60D when converted to FF equivalent. I wont be anywhere close to that with the FF so if the IQ is about the same, I will just continue using my 60D for extreme landscape photography.
It's always difficult to answer this kind of question without it seeming like a put-down, but the unhappy truth is that it's not worth switching to full frame unless you also have the budget for lenses. That said, you can't buy everything at once and the solution is often patience - wait until you have the funds for the right lens, which is undoubtedly the 16-35/4L IS. Buying the 17-40 would be a mistake in my opinion, unless you can find a very good used example for the right price. This is not to save money as such - it's so you can get most if not all of it back when you have the funds for the 16-35.
Regarding the extra FoV that you get with the Sigma - I don't think there is any full frame lens to match it*, though maybe there will be an RF 14-XX or 12-XX in the next year or two and when it comes it will very likely blow everything else out of the water! So start saving now!!
*Edit - from Canon that is. I assume you must have already discounted the non-Art Sigma 12-24, which is still available I believe?