Hervor Alvitr: Valkyrie of Wisdom

First up, go with the physical support.
Secondly, I think converting her into a magical guardian/tank would be better, since we don't have many tanks (plenty of mages and assassins) and we hadn't had a new tank (Vulcan rework doesn't count) in a long time. And yes, I know there aren't many Warriors as well, but I think that the last 10 gods, 7 of them were physical, none a Guardian, so...
Now as for the skills, If you decide to hear my advice and convert her to a magical tank, I think you'll figure out on your own how to change the abilities to a more supportive tank and less damage-ish.
Regardless, the abilities are all great, only one problem with the ult, as I disagree about reviving, but not protecting. So, instead try and consider to make the ult prevent a single death of one ally. I.e, lets say your ult is up, and you were teamed up with... Zeus. And the enemy gloriously balanced Mercury killed him, your ult will end and the killing blow of Zeus will hit you instead while he is healed by a % of the damage that was supposed o be caused to him. Something along the way of that.
Other then that, great job.

I really really like both kits, but i think that for the support role to work better, lowering the damage output (especially on the 2) would make her more supporty. Otherwise she could just be built all damage and still do wonderful.

I prefer the physical support, as I'm personaly not too keen on the assassin version. An assassin relies of heavy burst damage to quickly take out their enemies, but I don't really see her being able to do so.
Her first two abilities are defensive, sure, they are very GOOD defensive abilities, but I wouldn't say she needs both. I personally prefer the dash out of the two, as it makes her able to catch up to enemies ans escape, as well as give her some utility in fights.
Her 3...hm. Let's put it this way: It's kind of wierd. It deals decent damage, reduces the power of enemies and has a pretty long cooldown. As her only damaging ability, it is...wierd. I don't want to say bad, but to be honest, it kind of is. The fact that it reduces the POWER of enemies hit is also odd. It makes her even MORE survivable, which she doesn't need.

If we were to compare her to four other assassins:

Loki has great burst damage from his abilities and passive, and has a decent defensive ability.

Bakasura can take out enemies with the help of the massive penetration from his 1 and 3, which goes perfectly with his passive and ultimate. His defensive ability is also good.

Ne Zha is capable of taking out with the help of his ring, sash and ultimate. He also gains good basic attack improvements from his 2, and his passive gives him good sustain in the early game.

Thanatos is able to chase down enemies and instantly execute them. He is amazing: A percentage damage ability, an ability that makes it easier for him to catch up to enemies and damage them through their protections, an ability with good damage and a freakin' silence, as well as an execute. He also has incredible sustain and defense with his passive. Do I need to say more?

If you compare Hervor Alvitr to these four, you clearly see the thing here.
Q: What does she currently need? A: Damage or some kind of offense.

Q: What does she currently not need? A: More defense.

Now, another thing that I haven't even touched on is her ultimate. To me, it just seems underpowered. So, she gains movement speed, cc immunity and slightly increased range on her basic attack and third ability for 3 seconds. It also have a long 80 second cooldown.
It's just...odd, again.
It doesn't say how much movement speed though, so I can't really judge about that. Although I see some problems here:
1. The duration. It needs to be much longer, maybe not for the cc immunity, but the speed need a longer duration.
2. The cooldown. 80 seconds for this little? Needs to be shorter.
3. She doesn't need more of this utility/defense. Sure, you can use it to catch up to enemies, but for what? A 3 sec boost to movement speed with cc immunity, and with a 80 sec cooldown. Many goods have cc immunity on their ultimates (Apollo, Artemis, Anhur, Fenrir, Zhong Kui e.t.c.) but their durations are higher (about 2 seconds for Anhur, 5 seconds for Zhong Kui) and their ultimates have something better than a movement speed increase added to them.

I know you are creative, and I'm sure you can figure out something to do with this :)

BTW, I love the support version, although I think making her magical would be better.

I think I will change her Dodge to be something else. It already feels too much like Chang'e's move, anyway. Now you'd have a decent combo - Sundering Strike, then the new ability, then use Pressing Advantage to catch up.