Check the pinned post for direct comparison of frame data in PM to Melee on Samus' fire move set.
Unmentioned things in that data includes the timing/amount of invulnerability granted by AI from ledge is different in each game. In PM, the upair needs to be input at a later point, which means she has fewer invincibility frames. In regard to the priority of missiles, they haven't changed, as far as I'm aware. They beat needles because needles no longer have hurtboxes in Project M, which means one needle doesn't beat charge shot, either.
Samus now has access to crawling in morph ball, which greatly reduces her hurtboxes, and allows you to duck under projectiles and some grabs, as well as giving you access to boost ball, an incredible attack that sets up for pivot fsmash or grabs, and shield pokes relatively easily.
Another big difference is how Zair and tethers function in general. Zair can be used as an actual spacing tool in PM, as opposed to the limp-**** whip that you get in Melee. It's a great tool to use in match ups against characters like Marth or Ike, who can contest us at a reasonable range with their disjoint. Zair also beats out projectiles, and does similar stun to a Falco laser. It's a really ****ing good move.
You also have access to ice mode, which isn't really all that spectacular. It helps a lot for fighting Puff, as you have kill moves and kill setups on her with upsmash, but otherwise fire is typically the better beam to use.
If you've got any questions about stuff, just throw them at me, and I'll do my best to help you out. This was only a very brief coverage of some of the major things she has in PM.