Well, i'd expect an underwhelming growth of performance from multiplayer games that involve massive open world environments, this generally places a lot more stress to the CPU as oppose to the GPU.
Well, I do agree with you on the fact that having more frames is most certainly good, but getting frames higher than your monitor refresh rate wont really matter, especially in games like CS:GO. You probably know this already xD.
As for the spare money you have in possession, i'd ask myself on what games i'd like to play. 144Hz + 144 fps on a competitive game like CS:GO would definitely give you an advantage, but then again i did reach Supreme and held that rank for 2 months with a 60Hz monitor. It really would just depend on how much money you are really willing to splurge just to gain a keener edge in shooters and such, and it's not like you're reaching and maintaining a constant 144 fps at the moment in source games as you've said above.
If i were you, i would definitely choose the CPU + MOBO upgrade path. Would overall improve performance in all and every games. Any mid-tier i5s from the 5th-6th generation would definitely net you a noticeable performance gain. And depending on your budget, getting an i7 will also give you access to a lot more utilities and benefits outside gaming.
Can you give us the budget for your monitor upgrade/ CPU upgrade?