I am willing to bet that Ranger Vets are better trained than Paladins, and Anti-Material Rifles would certainly pierce weak points in Power Armor. But energy weapons would most certainly demolish the armor that Ranger Vets wear, and outside of the AMR, I don't think anything the Vets use would penetrate.
Depends on situation and equipment really. I think a Ranger could easily ambush and kill a Paladin, but head to head a Paladin would win.
No way Ranger Vets are better trained; Paladins live in an environment that raises them for war literally from childhood. They are a warrior caste, and their sole purpose is to fight. Nothing else. They are raised for this their entire lives. If you're a Ranger, you enlist in the NCR military at maybe 17 or 18, so a Paladin's already got years of training and conditioning on you. You go through crappy basic recruit training, spend some time as a grunt, and then finally get appointed to the Rangers. Meanwhile, the Paladin continues to receive the best possible training this whole time.
It's the same reason (cliche, I know, but it's the best anology) that the Spartans were the best Greek fighters. They trained for it their whole lives, from birth, to the exclusion of all else. Same goes for Paladins.
Ranger Vets may have more
experience than the new Paladins that have been cooped up in the Hidden Valley complex for years, but better
training? Not a chance.
RE: Shooting in the neck or eye- I don't doubt that a Ranger could accomplish that on a largely stationary target with ease. I
do doubt that they're going to be able to ace a Paladin through the eyes with no issues while that Paladin is moving with the full speed of Power Armor and returning fire. A Paladin can laugh off a hit to the extremities, while Vet Ranger armor offers literally no protection there.