Hi yexlm I have spent New Years eve in Amsterdam a couple of times and like most big cities it is very expensive. Expect to pay entry to large bars @ 20 euros, and night clubs @ 35+ euros.

Hotels are normally fully booked for that night months before and tickets to the best night clubs sell out quickly so be warned.

I always have a great time in Amsterdam as 'Ik spreek klein beetje Nederlands', (I speak a little bit of Dutch) and have some good friends there.
You will find the locals very friendly and they all speak very good English, oh they also love to set fireworks off in the streets on this night, a great way to start the New Year... with a bang!

I have never been to Dusseldorf so I can't comment on this city, maybe I go there for this New Years eve.

I haven't been to Düsseldorf but I do live in Germany so can give you a couple of tips about New Years Eve. Shops and cafes etc. close at mid day or 2pm so it is pretty dead in the afternoon, most restaurants that open in the evening only take customers who have booked a table, it's very difficult to find somewhere to eat if you haven't booked. There will be fantastic fireworks at midnight as most people spend a small fortune on them.