They both look as if they're suffering from dieback, which is a common affliction with Acer palmatum varieties. I agree the worst affected one should be removed, but with the other, prune out the dead parts back to healthy wood. Don't cut into healthy wood, Acers bleed at this time of year, make the cuts just at the point where the dead part stops.This plant may go the same way as the other one, but sometimes they recover.
I wouldn't worry about moving it - it's clearly getting enough sun to produce a good colour in the leaves, so insufficient sunlight isn't an issue. If you live somewhere with lots of sun and high temperatures in summer, Japanese acers suffer in full sun - it burns the leaves causing a frazzled appearance. Judging by the thickness of the trunk, it looks like these trees are pretty mature and may have been heavily pruned, which in itself can contribute to die back. If you've had some very wet winters and your soil is heavy, then verticillum wilt might be the problem, so when you cut off branches, split them open afterwards - verticillum shows itself as black streaks witin the tissues. It may not show in completely dead wood though, and there is no treatment for this fungal infection anyway.
In general, feeding isn't necessary, but it might be worth giving a balanced fertiliser to the one you're keeping to give it a boost. However,if your mulch is of organic origin, it's likely the plant already has all it needs. Some further information below
There is something I'm wondering about though; I can see white patches on the trunk (and branches in the almost dead one) but can't tell what they are - are they just lichen deposits?