Sure a totally new PC would be worth it, but then again I have this laying around doing nothing atm. So why not make use of it, if there is not much performance difference between the x58 and z87
Oh, that's different. But you said "Looking to buy a GTX 770, new PSU, Case etc.". And before that you said "I was thinking is upgrading my processor + motherboard + ram...". So naturally I thought you were wanting advice upgrading all 6+ items.
Depending on the processor you have now, the X58 platform can be almost as powerful as the Z87. But the processor would be the weakest link compared to today's. And if you want to go with a SSD, the x58 may not have SATA III. Then there's the purpose of the machine. Gaming? Productivity? You can go here and get a comparison of processors: http://cpuboss.com/compare-cpus