Deere used to offer most of the utility tractors in multiple configurations. Basically there was a low-utility, utility, and row-crop versions and multiple variations of each(sometimes also a mudder and high-crop version as well.) There are three tractors of the same size/vintage around here setup three different ways:
Our 2550 Row-crop:
-8/4 TSS transmission with independent PTO
-rack and pinion rear axle with cast wheels, 15.5-38" rubber
-wide adjustable front axle, 7.50-16 tires
-large row crop style flat top fenders
-deluxe lever release SCV valves and extendable lower draft links
Neighbor 1's 2550 in the low utility config (MFWD with loader)
-standard 8/4 transmission with left hand reverser, continuous running PTO
-flange rear axles, steel wheels, 28" rear rubber (I think they are 16.9-28's but not sure)
-mfwd, so obviously a different front axle
-small shell type rear fenders, deluxe lever release scv valves and non-extendable draft links
Neighbor 2's 2350 in the standard configuration: (2wd with loader)
-standard 8/4 transmission with left hand reverser, continuous running PTO
-flange rear axles, steel wheels, 16.9-30 rear rubber
-slightly narrower but still adjustable front axle, I think it has either 11L-15 or 10-16 front tires
-row crop fenders, standard style scv valves and non-extendable draft links
Obviously the row crop version is sold more for field work, the low utility more as a loader tractor and the standard utility as just an all purpose tractor. There is a big difference in ground clearance and overall height between ours and neighbor 1's 2550. Neighbor 2's is closer in height to ours vs the low utility. The drawbars can be turned up or down to accommodate this, not sure about differences in the 3pt. In the early years (10/20 series) they really sold them based on those configurations, when you get to the 30/40 series the definitions weren't quite as clear, and by the 50/55 series they were more 'option packages' as opposed to different models. I don't know if they used a different gear ratio for the different tires, but my guess is they did not. I do know that for the 2550 there is a 16mph tach/speedo and a 20mph tach/speedo, which I guess would correlate to tire size (ours uses the 20mph).
As to the OP, I'd be inclined to try mounting them up since you already have them. If you were buying new I would have stuck to the 15.5's for reasons mentioned (change in speed/gearing, 3pt geometry, etc). If you do want to go back to 15.5-38's I'm sure you could sell those 16.9's for a fair price.
Attached is a pic of ours in the row-crop config with 15.5-38's
