Let's say the following list is facing a mirror match and you win the toss :

Sear, TA-175, souless one 60pts

7 Vultures, grappling struts 7*20 pts

Do you take first player or not?

Pros : you have perfect information when planing your moves and can setup blocks to deny calculates. This can be huge if you can remove TA-175 from play.

Cons: Shooting first means that destroying vultures will grant a lot of calculates to the opponent that they can use both on attack and defense while yours can only be used in defense. In the endgame your opponent moving last can also let them roll out of arc.

This means that the first player should probably go for Sear first if at all possible, while the second player can choose to go for the vultures first if more convenient. Coming from a Tie swarm background my reflex is to take 1st player for blocks, but I'm starting to think that given TA-175 I should really go second.

Now for the bonus question : if there is a clear answer to the question above, would you remove a grappling strut for a mini 1 pt bid? Having a strutless vulture also gives you an advantage if you are trading vultures and can present it as bait since your opponent will have to destroy half a vulture more than you.

As you say, there are advantages to both. I'd probably give 2nd the slight edge for the reasons you mention, but I would probably make it less than a point of bid.

More reason to bid might be another matchup that would be considerably worse for you, but I can't think of any right off the top of my head.