First off, if I can play farcry4 etc quite happily on a 4gb system, I do question whether it is really the ram which is the issue given the types of games the surface lines are capable of playing (i.e nothing high end). What is it exactly that you're trying to play.
Secondly, I have to admit that it seems an odd question. The surface book and surface pro are very different machines, so seems odd to be deciding between the two purely for gaming purposes. What is the main function of the machine for you? That should be the deciding factor, with gaming as a secondary consideration.
well tried to run cod infinite warfare,i know its highly demanded game ,but the 4 gb ram was problem.
and some other games from windows store like forza motorsport 6.
anyway i like the gaming capability of SB and the cooling performance instead throttling issues of SP.
But i need the machine all the day with me for engineering job,so the kg of the SB its a bit negative.
trying to figure out which machine i should buy right now,i pretty happy with surface's all these years even now i use my old sp2.
i do casual gaming,just one hour per day if i have time,but i want to play some new games even at low settings/res , and keep at least 30fps.
I don't think there is any question, the dGPU in the SB will deliver a superior gaming experience. I used to carry around a SP1 with the power cover, so moving to the SB hasn't changed much weight wise. Using the SB with the screen turned around is also pretty close to using the SP if I need to prop up the screen (or even laid "flat", though obviously I could detach the clipboard as well). So for me going to the SB was a good choice. The full laptop experience outweighs the lighter weight and kickstand "lapability" of the SP, the SB can mimic a tablet well enough (though I do wish they could at least make a case with a wire kickstand or something). The SB power bump is pretty significant if you plan on doing any gaming, especially modern stuff.
But really, if you are price and weight conscious, you can make the SP4 work, especially if you utilize the fan tricks. But you seem to be quibbling over what, a pound of weight? Spend the extra 300 and do some push-ups, you will be fine