Yes, a gaming membrane will be significantly better than your non-gaming Logitech. It can take a lot of beating, and I mean A LOT.
Still its always worth going for a mechanical one over membrane one.
As the above post says TVS Gold is the cheapest mechanical out there, it's a decent one too, and the second one is the best sub 10k keyboard too, IMHO, I mean not the Rapid one, but the full one, which is known as CM QF Ultimate.