Veteran Sword-elf is a very strange card by design. Costing 3 resources for a 1/1/1/3 statline is not a good deal. 3 health is good and goes a long way in helping with blocking enemy attacks and soaking archery damage. Of course, one would not be running this card only for a 1/1/1/3 statline. Ideally, with it's special ability, it should higher, turning this elf into a killing machine. It's Noldor and Warrior traits enhance this aspect, allowing for some great interactions with cards such as Warrior Sword and Fair and Perilous.
The unfortunate issue is that its special ability is not that good.
Now, the card is by no means a complete right off, but it's intent and the way its design impacts play is strange. Allow me to elucidate.
The issues arrive from needing to have other copies Veteran Sword-elf in the discard pile for the elf to be worth playing. The first challenge is finding all 3 copies to get full value. Its viable with only one copy in the discard pile, becoming a cheaper, but less versatile variant of Haldir of Lórien. The second challenge is the cost. 3 resources is a lot. Paying this high cost should develop your board state substantially and provide value to help you win the game. Veteran Sword-elf does not provide this value and impact unless there is already another copy in the discard pile. Often, I find myself asking "if I had a different ally, would I be in a better position?". The answer is unfortunately in most scenarios yes.
Assuming best case scenario, Veteran Sword-elf will be a 1/3/3/3 with 2 copies in the discard pile. A good deal for 3 resources. However, with such high stats, ideally you should be making use of multiple of them, or one of them multiple times. This makes this elf an attractive target for cards such as Narya and Ever Vigilant. If you are not making use of multiple stats, then I question the value of having a fully powered Sword-elf. I'm not using it for questing, there are better options for the cost in sphere such as Meneldor. For attacking, I could use Marksman of Lórien. For defence, I could use Defender of Rammas or Derndingle Warrior, both of which are cheaper. And all of which are immediately powerful, without having to have 2 dead cards in the discard pile (how many times must I say some variant of Sword-elf and discard pile?? :) ). One way to view the Sword-elf is that the 2 copies in the discard pile are no cost "attachments" that buff the elf. However, you would get more impact by including a single copy of a good ally and 2 good attachments that can go on other targets instead of 3 copies of the elf.
Now, admittedly, this review has been from the perspective of playing 1 copy of the elf and buffing it with the other 2 copies. You can play the all copies of elf, with the intent that when the encounter deck becomes really mean and brutal and you lose a copy, you buff 2 copies of the elf. I do disagree. Squire of the Citadel is a card that provides value when he dies. And he is cheap. I shouldn't have to wait for a 3 cost ally to die before the other copies start to provide value.
Now, besides thematic reasons for running the Sword-elf, what sort of decks does this card belong? The elf does have value. Immediately one would think Noldor decks. The card cares about the discard pile (one half of the Noldor archetype, the other being discard).
Veteran Sword-elf does not quite work in Erestor decks. Erestor decks want to burn through their decks fast, which does ensure you power up the elf quickly. However, they also want to shuffle their discard piles back into the deck to play cards again with Will of the West. This results in the Sword-elf going through cycles of being strong to being weak. A tricky thing to balance and make work. It does however, work in Galdor of the Havens decks. You can stack the discard pile with any copies of the elf you have in your starting hand, then dig for the other copies with his activated ability.
There is another deck type that the Sword-elf shines in, although we haven't had dealings with them since the dark days. That's right! Dwarves! Particularly dwarf mining decks (discarding cards from the top of your deck). Dáin Ironfoot makes a great hero to run, allowing you to fill your graveyard with copies of Veteran Sword-elf. He is also in sphere for Stand and Fight, a good insurance policy for if you recklessly play minecraft with your deck and discard the 3rd copy... The classic Imladris Stargazer and Zigil Miner combo can help generate the resources to pay for elf's cost whilst controlling the mining and discarding of the other copies. Given that Zigil miner/Imladris Stargazer combo is used in non dwarf decks, the Sword-elf can be a fun inclusion in those decks.
In conclusion, Veteran Sword-elf is a strange card. There are undoubtedly better choices for that will win a spot in your deck in a competitive analysis. But there are decks where the Sword elf is a fun addition, particularly Dwarf mining and Galdor of the Havens decks. This elf has it's problems, but I encourage you to include it in such decks, get it out of the binder and have a bit of fun.