Well.
If he is able to handle 480p@30, can I do same? with my Core2Duo E8400 3,0GHz 6MB L2?
https://obsproject.com/forum/threads/configuration-for-stream-on-core2duo-e8400.33581/
depending on what you wrote you two try to achieve completly different goals he would use a less powerful cpu to ONLY stream (streaming machine) playing on console thats the reason he could maybe be able to output 480p30 but you are actually trying to game+encode on the same machine which will simply not work with your cpu