It's hard to answer your question because you're asking us to predict the future. What field will be saturated, what field will be in demand?
Right now, pathology and radiology are saturated fields .... a few years ago they were not (and were in demand). Heme/Onc is starting to become saturated (according to my heme/onc friends). Nephrology is a tough market. There is a shortage of pulmonologist/intensivist nationwide.
Once you pick your field and complete your training .... the market may be completely different. There may not be any openings, or there may be tons. It's hard to know. What is true now may not be true tomorrow.
Medicine doesn't really follow simple macroeconomic principles (such as supply/demand) so it's hard to predict the future due to too many outside influences affecting the market.
By the time you complete residency, your priorities may change. You may have wanted academic medicine, but decided you hate academic culture or you want more money. Or you may have been fallen in love with academic medicine, teaching and doing research. You may want to move to cross country to your ideal location, or you may already have family and your spouse does not want to move due to variety of factors (jobs, family, schools, moving the kids, house payments, etc). Or you may have no choice to move because the market is saturated.
A lot of people stay within the same geographic region as their residency/fellowship because they are familiar with the area, know the practices (and the reputation), know the resources of the area (not just health/medical resources, but other stuff like things to do on weekends, good schools/bad schools, etc). They may have picked that residency/fellowship because of family (or desire to be in the area) and have no desire to leave. It's also easier to establish network and connections to area docs while in residency (and can establish a good referral base once you leave training). Then there's inertia - some people don't want to move again. Then there are people who can't stay still. The area docs (and practices) also know the type of training that you received. It's a bigger variable if you look outside the region unless you come from a big-name place (ie Mayo, MGH, Hopkins, UCSF, etc) - but then the fear from private practice groups is that you're not ready for the demands of private practice (PP and academia are different beast)
However, the one constant when looking for a job - No one cares what your USMLE or COMLEX scores are. No one cares if you are ranked in the top quartile or bottom quartile. No one cares if you are a DO or MD. What they do look for are: Are you board certified? Do you bring the skills/expertise that the business needs currently (either to fill a gap or to expand)? Are you a crazy loon that can't work with any office staff, or patients? Are you a danger to patients? Are you responsible?
Long winded answer, that doesn't really answer your question, but I hope it gives you some insight/perspective.
*an open secret that a lot of premed don't know - if you work in academic medicine (Mass Gen, Duke, Hopkins, etc) - your pay will be significantly lower than your private practice counterpart. A 2008 MGMA survey showed that academic primary care compensation was $158,218 compare to $186,044 for private practice primary care. For specialties, academia pays $238,587 compare to $339,738 for private practice.