In 'The Ultimate Computer' the Enterprise destroyed another Constitution class ship, the Excalibur, with just a couple of phaser shots at distance. 
While it may not shatter a planet to rubble like the Death Star, I do think the TOS Enterprise was fully capable of devastating a planet, turning a thriving ecosystem into an airless wasteland easily.
	
		
			
		
		
	
				
			While it may not shatter a planet to rubble like the Death Star, I do think the TOS Enterprise was fully capable of devastating a planet, turning a thriving ecosystem into an airless wasteland easily.
 
				 
 
		 
 
		 
 
		 
 
		 
 
		 
 
		 
 
		
 
 
		 
 
		 
 
		 
 
		