Quick maths, the odds of forcing an armour save are:
(number of shots) * (chance of hitting) * (chance of wounding)
Adding in a typical marine reroll aura is normally going to be rerolling 1's only. Rerolling 1's improves the odds of success of that roll by 7/6 - so in almost all cases it makes no difference whether you use a captain or a lieutenant.
Using your example of hitting on 3+ (4/6) and wounding on a 4+ (3/6) would look like this:
No reroll aura:
1 * (4/6) * (3/6) = 1/3 of shots force a save roll
With a Cap:
1 * ((4/6)*(7/6)) * (3/6) = 2/5 of shots force a save roll
With a Lt:
1 * (4/6) * ((3/6)*(7/6)) = 2/5 of shots force a save roll
Sniper weapons generally have a mortal wound option on the wound roll though, so in practice a Lt is slightly better at buffing Eliminators, but a Phobos Cap also has a sniper weapon and forward deployment ability to actually contribute with.
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