The pros would be you'd never need to buy gas for the chainsaw.... that's the end of my pros list. Oh, also, it's quieter.
Some cons would be:
Expensive saw
Tethered to the tractor by limited hose length
Storing hose between uses/moves
Not as maneuverable as a stand alone saw
Unknown Gallons Per Minute/PSI requirements of saw and output of tractor hydraulics.
Tree trimmers in bucket trucks use them fairly often. But they are limited in the reach from the bucket, so stand alone is not important, and, the hoses add a measure of drop protection as well. Down on the ground, they use gas powered saws.
I'd rather have the tractor free to move firewood/logs around and not have to stow the saw every time I had to move the tractor, or move the tractor every time I had to move the saw.
One neat thing, though, is that they work underwater.
I thought I read somewhere that they use a bit of the hydraulic fluid to oil the chain, so if you cut a lot, you'd have to keep an eye on your tractor hydraulic fluid level. Some days I'll go through a couple quarts of bar oil.
So just some things I've noticed over the years.