All the prestige sprints are the same, just with different animations. If you actually use sprint all the time, consider it an early form of power customization.
Yes, once you pick between SoM or the GSA, it is permanent. I usually go with SoM because you can attack multiple targets with it and it has a great debuff. For my non-combat-oriented or non-melee characters, it still has use later in the game.
The axe is nice, but you don't often face true undead in the early game. By the time you do, you'll probably have a decent attack chain that doesn't often have room for the axe. When I get it, I save it for BP or CoT spectrals. IMO, go for the Sands. 
There are no words for what this community, and the friends I have made here mean to me. Please know that I care for all of you, yes, even you. If you Twitter, I'm MrThan. If you're Unleashed, I'm dumps. I'll try and get registered on the Titan Forums as well. Peace, and thanks for the best nine years anyone could ever ask for.
Note that when you claim the Prestige Sprints - they ALL show up in your Powers Window and you can't get rid of any of them, although you can, of course, remove the from the Powers trays.
That can be a bit annoying because they make the right-side bar of the Enhancement screen quite long.
The various Sprints can give some nice visual effects, and if you squint just a bit make it "seem" like you are going really fast.
I also usually take SoM as the Vet power, mainly because I hate redraw.
Altoholic - but a Blaster at Heart!
Originally Posted by SpyralPegacyon
"You gave us a world where we could fly. I can't thank you enough for that."
You will eventually have the opportunity to pick up whichever power you didn't pick, albiet very much later, at 54 months.
There is another temp power choice at 33 (Blackwand or Nemesis Staff)
54 then gives you the choice between the 2 powers you didn't pick previously.
So, I officially reached my 12 Month Vet Badge.
In checking on paragonwiki, it states you get some pre-ordered sprints: Prestige Power Dash, Prestige Power Quick, Prestige Power Rush and Prestige Power Surge. In reading the description for those, they all seem to be pretty much the same but maybe with a few different effects.
In addition to that you get 1 Free Character Slot Per account, Temporary Power: CHOICE: Permanent Ghost Slaying Axe or Permanent Sands of Mu, Base Item: Weapon Displays: Arachnos Guns, Arachnos Mace (Floor), Arachnos Mace (Wall), Circle of Thorns Weapons, Gun Rack 1, Gun Rack 2, Jack-in-Irons' Club, Longbow Weapon, Mallet, Nemesis Rifle, Rikti Rifle, and Sci-Fi Rifle.
With all that being said, does anyone have any opinions on what's best to take as far as the Ghost Slaying Axe or Permanent Sands of Mu and which Prestige Run do you think gives the best special effects while moving? Not sure if I did pick one of those temp powers such as the Ghost Slaying Axe or Permanent Sands of Mu if I would never have the opportunity to choose the other one being that I am not sure if it is locked in until I reach another Vet Reward?