the 1 year MBA (usually called executive MBA) and 2-year MBA are largely different beasts. the 1 year MBA is mostly for people who don't intend to switch career paths (or even companies) post MBA. it also applies to people who have a family business or something similar, and are looking to head back to the same place after they're done.
by and large, the 2 year MBA is for people looking to switch either function, industry, specialization or any combination of these. there is a formal recruiting process for students in the 2 year program; i'm not sure there is the same thing for a 1 year MBA program (since the schools expect you to already have your post MBA goals set out).
i do not believe that the GMAT is required for 1 year MBAs. I don't know the firm numbers, but if i had to guess, I would say that the 2 year MBA is more selective since they draw from a much larger applicant pool.
keep in mind that you would normally need a significant amount of work experience to be eligible for the 1 year program at most schools. for kellogg, i believe you need 8 years of full time work experience.