The i5 is a better value for gaming compared to the i7. (Basically what Neezon said)
As for storage don't forget you can bring the storage from your older PC over. Unless you have something else in mind for that PC.

In terms of AMD vs Intel I always tend to see it like this:
AMD = Productivity (Tends to have better multi-core performances)
Intel = Gaming (Tends to have better single-core performances)
For what to get I would go to the i5 simply because I like intel more and also there's more storage in that build.
Also looking up some reviews between the 2 could always help you choose. But you should see they end up performing about the same with the i5 slightly edging out the 2600x. (I always use reviews to at least compare.)
Uses a small amount of major game titles.(graphs start at 0:30, Gaming graphs start at 1:10)
This review uses the GTX 1060 6GB with major game titles.(Graphs start at 0:30)
This last one I'm only throwing in there because it can kinda show the performance of major esports titles for the i5 8500. The review uses a i5 8400 instead (about the same fucking CPU) and a Zotac GTX 1080 Mini. Also a typo happens in the review on the CSGO graphs the Min and Max framerate numbers are swapped for the i5.
Major epsorts titles (Graphs start at 0:41)