In the market for Kitchen Cabinets. I have two quotes from two
different cabinet brands for the same kitchen drawing. How do I find
out if I am getting a better quality cabinet for higher price?. I Want
to be sure that the lower price of the cabinets does not mean lower
quality as well. Please list the criterion I should look for in
situations like this.

In my choice of kitchen cabinets, I would rate (1 to 5) at least 3
suppliers according to the following:
1)materials - choice of material such as wood, post formed, plyboards,
plywood, laminates, etc.
2)workmanship - build quality of the joints, miters, lapping, etc. and
finish of the surfaces
3)accessories - rate the handles, knobs, hinges, slides used on the cabinets  
4)function - although cabinets' main function is storage. rate how you
access the goods, the opening and closing, from simple swing to
vertically folding cabinet doors, and ease of use
5) aesthetics - seen from a distance, are the cabinets proportioned,
balanced, tastefully painted/colored/designed?
6) price - quality is never cheap, but nowadays, high tech equipment
and machineries can drastically lower the producton cost without
sacrificing quality. go for the best value for your money

You may find this link useful when planning a kitchen
http://www.forteelectric.com/KitchenRemodel.html