Been awhile,, but if I remember correctly, 300 series stainless will oxidize very little as in loosing it's shine. 400 series is somewhat magnetic and will rust some on the surface. 300 will polish up nicely, hold a shine better, but is easily scratched (in comparison).
The 300 series is what we used for cold forming / drawing when a lot of stress wouldbe placed on the material (softer and more fluid like). The 400 series would "work harden quickly and crack and tear if stressed overly much. Of course that's all relative. They all have limits to some degree. The 440 stuff is used for knife blades because it can be hardened and hold an edge longer than 300. Over time it will take on a rust patina, but not as bad as some of the other 400's. 416 I believe was bad at rusting in comparison.
300 has more copper/nichol, more pliable, and usually used for better quality pots and pans, etc. for the drawing qualities needed to get the depth.
From my experiences in the comercial fishing industry, generally speaking, above the water line, tanks, etc. that didn't mind minor rusting was 400 series. Below, valves, lines, etc. 300 was preferable.
300 is considerably more expensive than the 400 too.
Hope that helps a little.
Gary
PS; Stainless should transfer the heat / cold better than aluminum because of being more dense. S.S. coolers vs. aluminum & Plastic.