Pro's -
big tire, big tire volume, big ballast. Mine are filled with RimGuard. A 16.9x24 holds 653 lbs of fill each, the standard 13.6x28 'only' 460 lbs each. In addition, these particular 16.9x24's that Deere provided are heavier 6 ply vs the stock 13.6x28 4 ply, there's quite a bit of difference in carcass weight which makes the total combined weight/ballast difference nearly 500 lbs. over the smaller tires. So, I've got lot's of rear ballast and overall tractor mass, for better or worse (at times). I haven't run it past a scale, but my 4710 without the loader is probably up around 4900 lbs. With the 460, hd bucket and toothbar mounted, it's probably over 6000 lbs.
I would also assume there are differences in how the two sizes will 'dig' or 'float' in various soils but I've yet to really get mine so far into the muck to guess on that.
Cons -
Since the tires are notably wider, for any given wheel/rim position setting - the tractor is both wider overall, and has less 'clearance' between the tires. I have mine set at a 55" track, which makes the tractor just about 72"-73" wide overall, not a bad match for the 6' MX6 or the loader bucket. However, that makes the between-the-tires clearance about 37"-38". Not a big problem working around the 3-point, but I wouldn't want it any more cramped.
Also, if you have any intention of doing any actual light farming - that narrow between-the-tires clearance and individual tire width comes into play dealing with windrows, row or bed spacings, even moldboard plow size/spacing so that you can fit in and align with the furrows. There the 13.6x28 might have a small advantage. Most owners would probably never run into an issue there, though.