Most people will be satsfied with IRLB8743 or IRLB3034 MOSFET's unless they spend a lot of money on a good SSR. You have to check the specs of the SSR to see what the On Resistance is or the expected votlage drop to fully decide. The MOSFET solutions work well as long as the PCB runs, connectors, and wires are all good quality and heavy duty. Some of the cheap boards skip on the connectors, runs, and even the MOSFET's. As I pointed out to someone else in another thread MOSFET RDSon at 4.5V is what you need to look at for MOSFET select vs it's price and your wallet (IRLB8743 is a good solution at low cost, IRLB3034 is even better but costs more).
It's a good idea to see where you are loosing voltage under full current load to decide what is at fault. Let that be your guide in deciding.
It's a good idea to see where you are loosing voltage under full current load to decide what is at fault. Let that be your guide in deciding.