Good start I suppose...what games do you play? What kind of performance improvements do you seek?
What is your interest in upgrading to 8.1?
Windows 8.1 is more efficient in how it handles just about everything versus 7, so yes it's a snappier and faster OS overall. Will it be night and day difference for you? Maybe...maybe not. Depends on how you configure your system, what you decide loads at startup, if you have an SSD or SSHD for OS duties, etc. Those all can make a difference.
Honestly I noticed overall that 8.1 was a smoother and snappier experience, and after getting over their lack of the Windows 7 glass-style interface which I loved for the simpler 8.1 interface which I now prefer, I was pretty happy. Memory consumption seems to be about the same...but in research I did when looking into upgrading to 8, I found a couple articles about how 8 handles memory better than 7 in a couple different ways that should translate into stability and performance improvements.
I also like the fact that Windows 8.1 Pro includes Hyper-V, and I've used the hell out of that, and transferred VM's between my Server 2012R2 server and laptop or workstation with ease.
Windows 8.1 as a total experience to me is smoother than 7, there are some things I don't use like the Metro interface, being replaced with a bypass in Classic Shell (Free, get from Ninite.com with other good utilities), and I didn't like when 8 would force a reboot for pending updates if you didn't after 3 days. That was a stupid move that they've since resolved thankfully.
Beyond that, whether connected to a domain or not, 8.1 is awesome, I play old games, new games, it all runs great... but for strict performance comparison, I go by what works for me...and both 7 and 8.1 do...but 8.1 does it better. Especially on my laptop, where its efficiency improvements really help out with OS loading, program/game loading, power saving, etc.
Hope that helps!