Remington's site says 5-3/4 and 6 so I think weight is a wash. The 6-3/4 number might be a loaded weight.
Option 1 has a choked barrel which increases flexibility a bit.
One other issue to think about is whether that extended mag tube on Option 2 is going to make it feel front heavy. I have a 12 ga. 870 that came with the extended mag tube. I took it off to go bird hunting (with a longer, choked barrel) and haven't put it back on. I've preferred to give up the extra 2 shell capacity in favor of better balance.
So if you've verified that the shorter LOP fits the both of you then I'd go Option 1.