Woody, it may depend on your location and the source of your logs. I am in the metro KCMO area and we are at the edge of the eastern hardwood forest range of the USA. The only native softwood we have is Eastern Red Cedar (which is actually a juniper). That means our "utility" species are all hardwoods, something like hackberry, rougher oaks, cottonwood, soft maple, etc. Longer to dry, harder to nail, logs more expensive to buy.
Around here, normal prices of SPF lumber from box stores like Lowes, H-D, and Menards is very competitive when you consider log prices, milling costs, drying to a useable moisture content, and planing; even if your building codes don't require grade stamped lumber for construction.
If you live in an area of the country where you can get suitable species for construction lumber (SPF), at a reasonable price, and do not need to meet code restrictions, then sawing out your own shed may make sense. I doubt that the price would change much by diameter unless you are very picky about what diameters you will buy. Otherwise, I would think that logs that square up to a incremental cant size would be your goal. Max cant size would be 70% of SED (small end diameter). So, if you were targeting a cant wide enough for 3 stacks of 2x4s (~18 2x4s), or 2 stacks of 2x6s, you would need a 12" wide cant - that would require an 18" diameter log (18"x .7 = 12.6"). A 17" log would leave some want on the corners of 4 pieces. That is assuming the logs are straight. For 4 stacks of 2x4s (16" cant), you would need a 23" log (~32 2x4s). Those are projections, in actuality you probably just need to take what you can get from the logs you can acquire. Another B20 owner (2007).