I've stayed at the Polynesian 4 times and the Contemporary Concierge twice and if the choice is between the two I would choose the Contemporary Resort.
Both are great and Polynesian is themed better, but that monorail running through the Grand Canyon Concourse just takes my breath away.
I think the shops are better at The Contemporary.
Both have great places to eat but I prefer The Food and Fun Center at the Contemporary Resort over Captain Cooks at The Polynesian.
To me a pool is a pool so I don't prefer one over the other.
If the choice is a reg room at the Polynesian over a Conceirge room at the Contemporary I'll take the Contemorary every time. The free Breakfast buffet (I know...it's not REALLY free)and the snacks during the day are great!
But I'd take Polynesians Conceirge service over the Contermporary if that were the choice.
If you stay at a Polynesian Resort Longhouse that is far from the Great Ceremonial House, and there's a rainstorm, you are going to get wet.
At The Contemporary Resort you are always under a roof or in hallway , protected from bad weather.
Lastly, I prefer The Contemporary Resort over The Polynesian most for this reason: After The Magic Kingdom closes, and the throes of people are flooding out the exit gates, rushing to get on the Boats, busses, or the Monorails, if You stay at the Contemporary Resort, you just avoid all that mess and just take a nice, leisurely, 10 minutes stroll back to your resort.