While I agree with most of what is been said and Nomercy's what if scenario's, the SAAMI specs for reloading books today have dropped off a solid 100 fps on almost every caliber listed. I have some older books 40+ years old that have some interesting load data. That being said knowing how to reload and using the right specs is going to be a lot more important than Remington vs Winchester brass. Because in the normal scenario's of reloading the SAAMI specs are not going to get you blown up. Now as mentioned before different powders, primers, bullets and seating depths might cause you issues if your new to the reloading world. There is a reason you should own a caliper and a powder scale while reloading. But what if your scale is not right and you don't know how to calibrate it? Some powders will vary +/- 2 grains through a powder measure if you don't throw the arm the same way and speed everytime. Some powders will do that regardless. Lots of variables, to the new guys I say stay well under max loads until you learn to play the game.
Saying all that I have stuck a bolt in a friends gun using my loads that work well in my rifle and are under max by 2.3 grains according to today's SAAMI specs. Chambers and actions also play variables on these scenario's. Do not put a friends reload in your rifle and do not load for other people unless you have the rifle in hand to test loads as you go. You truly need to work up loads for each individual rifle. Lots of variables folks lots of them. The cheaper the components, equipment and firearm usually brings out the most interesting results.