Snipers and rocket guys will test if you ignored your Strenght
How so? Seems to me I'd want speed to spot and countersnipe them, not strength. Maybe I am missing something strength does, but it seems like the least useful stat. Speed is just great in general, willpower fuels your abilities, most of which are incredibly good and strength just lets you deal more melee damage (just use a shotgun) and carry more (It's not like I can afford to outfit everyone with enough backup grenades/weapons to max out either way). Strength does help you resist paralysis, which is good. But the attacks which cause it inflict a lot so it feels very expensive to bump strength just to get an extra ap in those edge cases.
Strength is best stat. Each point of strenght improves: Max HP (1 = 10 ), Paralyze resistance (1 = 1), Throw Distance, max Encumbrance (if you go over max you lose Speed, 1 = 1), melee damage with Bashing (damage = size of weapon x Strenght score, max can be 5 x strenght).
Speed will not help you vs enemy snipers. Only luck or enough HP to survive being one shot can (or hit once with that and then by some other person taking a pot shot at a weakened soldier).
I already had so many situations where my soldiers would have died if my Strenght was 1 or 2 points lower and I got 500+ hours of playing the game.