Answers

The small walk in pantry will be the less expensive option. However, having a cabinet that functions as a pantry is often a better use of space and ends up as the more preferred option by my clients.

But it's all about you (or your client)! What would you/they prefer? Is the storage space best utilized with just simple open shelving? or would it be organized best with pull-outs and drawers? There are obvious pros and cons to each, in my experience - the extra cost of a cabinet wins 90% of the time. 

If you have the extra space, and depending on its use, a walk-in pantry is a luxurious upgrade. In most cases, where floor space is at a premium, pantry cabinets are the best bet. Looking a a bank of finely crafted cabinets is also much more applealing than a closet door.

As for cost, you get more for your dollar with cabinets as well. Framing a drywall closet with fixed-shelves may be slightly cheaper, but much of that cost is labor. We advise the client to put the money in the product.

When you add pull-outs to anything the cost rises exponentially. It's improtant in the design process to determine a good balance between accessibility and organization to avoid unnessisary cost overruns.