Pros:
Lots of power to be had at extended range.
Common caliber so factory ammo is readily available
An accurate caliber with lots of handloading components available - Data, bullets, brass, primers etc
Not going to be obsolete anytime soon - In service with U.S. Army.
Pretty good resale value as many still like the 300 as a premier hunting cartridge
Cons:
Not a caliber for the faint of heart or folks who don't practice regularly - especially with hunting weight rifles
Tends to be at the point of diminishing returns. High blast and recoil for a moderate increase in performance.
Hard on throats. Barrels will lose their accuracy edge fairly quickly compared to other calibers.
Used to be that the 300 was a distinct increase in hunting performance, now with modern loads for the 30/06 - not so much.
Factory ammo is quite expensive relegating it more to a handloaders cartridge.
Other modern calibers deliver the same target accuracy performance at the same ranges with less shooter fatigue.