System Requirements for Windows 7 and 8 are the same but Win 8 does a bit faster, and without the background apps it should do even better... But your hardware exceeds the system requirements for Windows 7 so maybe you should try finding the cause for it running slow... To begin, start disabling startup applications from msconfig typed on Start / Search or Start Run... then on msconfig / Startup tab; uncheck all but the antivirus, next on the Sevices tab, mark "Hide all Microsoft services" and uncheck third party services except for the antivirus. After that run the Antivirus and follow with Malwarebytes Antimalware, to remove possible malware/virus that may be causing your system to run slow.
Windows 7 system requirements
http://windows.microsoft.com/en-us/windows7/products/system-requirements
If you want to run Windows 7 on your PC, here's what it takes:
1 gigahertz (GHz) or faster 32-bit (x86) or 64-bit (x64) processor
1 gigabyte (GB) RAM (32-bit) or 2 GB RAM (64-bit)
16 GB available hard disk space (32-bit) or 20 GB (64-bit)
DirectX 9 graphics device with WDDM 1.0 or higher driver
Windows 8.1 System requirements
http://windows.microsoft.com/en-GB/windows-8/system-requirements
If you want to run Windows 8.1 on your PC, here's what it takes:
Processor: 1 gigahertz (GHz) or faster with support for PAE, NX, and SSE2 (more info)
RAM: 1 gigabyte (GB) (32-bit) or 2 GB (64-bit)
Hard disk space: 16 GB (32-bit) or 20 GB (64-bit)
Graphics card: Microsoft DirectX 9 graphics device with WDDM driver
If you do decide to install Windows 8.1, install these two programs, 1st one to lighten it up and 2nd to make the Start menu more functional and disable the Windows 8 Charms Bar and some features that take up system resources.
Uninstall preloaded Windows 8 apps in bulk with this program
http://www.pcworld.com/article/2148482/new-app-automates-the-process-of-dumping-windows-8-metro-bloatware.html
Classic Shell Start Menu
http://www.classicshell.net/