We should ask what problem you're trying to solve. Is this simply a snow issue? Or is this a multi season tool? What's your budget? What do you have now that's not working, and how is it failing you?
A good pair of boots is a solid choice to start with, but the right ones are more expensive than a pair of gaiters and the boots you own.
I have no experience with the OTTE gaiters. A few friends own the Tasmanian tiger ones and don't mind them but they slip out from under foot.
I've used a cheap pair from MEC, and have a pair of OR expedition crocodiles. Both do just fine keeping snow out in the winter, and debris/mud out in the shoulder seasons. Solid protection almost to the knee.
Crocodiles are a bit easier to put on.
I'd be interested in hearing what the problem is you're trying to solve. That should help us better suggest a product.