Sheiko shouldn't advance your #s any faster than 5/3/1, necessarily. If you were able to follow 5/3/1 for a year without missing a rep, you'd put 120lb each on your deadlift and squat. I don't foresee much more improvement over one year with Sheiko at your #s. Maybe your bench would get more improvement, it's hard to say without knowing you better.
I think a better question isn't which program will give you "faster gains" but which program best suits your goals. Are you or do you plan to be a competitive powerlifter? Or are you just trying to get stronger for other sports/the hell of it?
Sheiko is very sport specific, whereas 5/3/1 is more adaptable. Hell, even Westside is more sport adaptable than Sheiko. So, if you want to be a competitive powerlifter and that is your main goal, I would at least give Sheiko a try. If you are just trying to get stronger for its own sake, I would recommend 5/3/1 or any host of other S&C programs, as you will be able to adapt those more to your goals than Sheiko.
Just my 2 cents. Full disclosure: I've run 5/3/1 for over a year in the past, but have not tried Sheiko, although I have thoroughly researched it very recently.