I think it really comes down to style (your character class, gameplay style, etc.) and how either of the two horses compliment your gameplay. I feel that Arvak is perfect for mage characters, especially vampires (mage or otherwise), as well as for conjurers/summoner mage characters.
To compare the two horses:
Shadowmere will respawn at the location he last was killed or died at, or at the pool outside of the Falkreath Sanctuary. However, you do have to wait at least 10 in-game days for this to happen. Arvak is a summon spell that when he dies, you can just resummon him without any risk. Due to this, I feel that Arvak has far more utility than Shadowmere.
Despite that Arvak requires DLC, a related side-quest that can only be done after a certain point in the Dawnguard main questline in the Soul Cairn and requires learning a spell to summon the horse; I think that it is all worth it because the Dawnguard DLC is a well written storyline, gives you both a free mount and an awesome follower (Serana).
Arvak, himself, is easier to travel with due to the fact that you don't have to have him with you at all times. You can just summon him, ride him, and then kill him or use a Banish spell to send him away. If he dies, you can summon him again, if and when needed.
Shadowmere cannot travel with you to Solsteim, while Arvak is a summoned mount, that does not get in the way like other mounts would while traveling (as you can just kill or Banish him and not worry about losing your trusty steed).
So with all that said, Arvak has more utility and hence is more useful, while the tasks to obtain him are not that difficult at all. Also, Arvak is a blue-purple colored, flaming, undead skeletal horse of awesome, perhaps making him the most unique horse in the game, compared to that of Shadowmere, who is just a jet-black horse that has a few unique features.