I use .308 and .243 and have tried a large number of bullet designs and velocities in my homeloads. Meat damage has not been a problem with either and each shoots flat enough for ethical maximum range shooting. By this I mean that the limiting factor for me taking the shot is not the excessive elevation correction but time-of-flight, quarry movement, wind etc.
The .243 is a versatile round but I only use it on land where the police have stipulated (somewhat arbitrarily) that anything "larger" must only be shot from a high seat. I shoot mainly woodland fallow and they are a pretty chunky lot in my neck of the woods.
The .308 doesn't seem to cause anymore meat damage than .243, even with appropriate ballistic tips (never less than 150grainers, as the lighter bullets are designed to be too frangible and don't give controlled expansion/penetration in deer). I also shoot Roe and the meat is fine if appropriate bullet and shot placement are used.
The .243 has accounted for many large deer but I have had to search for a bullet that behaves. My initial load used 100gr Speer SPBT, which were accurate but didn't exit. Weight retention was usually less than 45% and the jacket would often separate from the core:
I tried 100gr Hornady's Interlock, BTSP and SST, Nosler's Partition and Sierra Gameking and Prohunter (amongst others.) None have proved 100% satisfactory for Fallow buck or even large female. By this I mean that the round has not reliably exited despite not hitting shoulder on entry or exit, only rib. With one notable exception, none of the animals have suffered or required a second shot. The exception was a solid fallow buck at which I took a high heart shot. He barely flinched and even carried on toward me. I was worried I must have lost zero on the scope and wasn't going to take another shot, I assumed I had missed cleanly. I watched him through the scope and as he neared, I could see a patch of ruffled hair on his side which matched my shot placement. He sauntered closer and I decided to take a neck shot as he showed no unsteadiness and was close enough. He dropped cleanly.
The gralloch revealed the ventricles of the heart were shot through with the first shot: (The left of the two hearts in this pic):
Incidentally, the heart is very tasty when not damaged.
I have felt uneasy shooting larger species with .243 since then. The .308 is a nice short action, easy to handload and not too kicky. It has always done the job and left enough exit to track deer that bolt 100 yds into cover despite a clean shot.
I had thought bullet construction and placement was the main issue at the heart of the "calibre" debate. I do think "too much gun" is rarer than "too little" in UK deerstalking.
I'm going to stick with .308 but will, at some point, try .260 or 6.5mm on the land with the strange calibre restriction.