Hi - these are my two favourite resorts and I've stayed at both when my children were the same age as yours - so hope i can help. I am a DVC owner but have only stayed in WL hotel, not the villas - can't help there aside from to say DVC villas are lovely and spacious.
I have just made the decision for our three nights before the cruise - and i chose the Poly because of the monorail. Had I been staying for a week, I would have gone for WL. Concierge may be worth it for you for the snacks and drinks - especially with young children.
The poly has no hot tub - the Wilderness Lodge has two. The Wilderness Lodge also has a toddlers paddling pool. I don't recall the poly having one - although i would imagine your children would wear water wings. Still, it is fun for them to paddle round in the small WL pool.
Transportation from the poly is obviously the quickest for the MK - but if time isn't a great factor, the WL boat trip to MK is lovely, and we have never had problems with the bus service there.
Rooms at the Poly are larger - am unsure about the deluxe rooms at the lodge. But, you can get rooms with bunk beds at the lodge - if your children are both in beds. If the youngest is still in a crib, it may be a little bit of a squash with a crib in the room.
Theming at the lodge is probably more dramatic and has the edge over the poly slightly. But, the poly still has excellent theming. Both resorts are lovely and relaxing.
Concierge might be nice with children the ages of yours, as they could play in the lounge, whilst you relax.
It really is a tough choice and i would say if you are making a short trip go with the poly - and if you need a crib, you will have more room then. You will enjoy whichever one you stay at.