Welcome to the forums!
I'm not too familiar with either of the bikes you mentioned, but keep in mind that once you get over about $500, the lower end components are still perfectly serviceable. And when you have two bikes at roughly the same price point, the spec and quality are about equal, so it comes down to personal preference, and maybe SRAM over Shimano or RST over Suntour. Unless you get a closeout, no one brand is really a better value than another.
That said, Giant is the world's largest manufacturer of bicycles, and Jamis is a relatively small brand. Raleigh doesn't have a lot of presence in the US, but they make good bikes too.