I have just run New Idea pickers so you can take this for what it's worth.....
From what I've heard from others:
John Deere 300 Picker
Advantages: less shelling on the row since the picker header has stripper plates
ability to change header easily from 2 to 3-rows and wide/narrow rows
Disadvantages: takes more horsepower
doesn't husk as clean as a New Idea
generally more expensive to purchase
New Idea Superpicker
Advantages: can pick corn with practically any horsepower tractor
does a better job in down/tangled corn
can be purchased for not a lot of money, especially if you can use a wide-row model
Disadvantages: snapping rolls can shell corn quite badly on the row, especially if the corn is dry
to change row spacings you must get a different machine
I don't think the New Idea has a better husking bed than a John Deere, it just pulls out more trash at the header so the husking bed has less work to do.