the 6.5x55 in general loads heavier bullets and is more akin to full sized rifle catridges. It belongs in the same grouping as .270, 7mm-08, 7mm mauser, 30-06, and the like. Sure, it is probably at the bottom of that line, but that is the family it belongs in.
When looking at what it does on that end, it will outperform the .243 on deer and elk and black bear.
But that isn't the beauty of the .243, the 243 is supposed to overlap, it is supposed to give mostly the same performance as the 6.5x55 against deer sized animals, and it does. (but not when you step up to elk)
where the .243 shines is that it is also a great flat shooter for antelope, coyote, prairedog, and the like. The 6.5x55 with a 120-140 grain will be in the same ballpark as the .243 with a 100 grainer, BUT the 6.5x55 has got NOTHING that competes with the .243 using 55 grainers.
Yes there is overlap. But in truth the 6.5x55 is overlapping the .270 and the 7mm-08, etc. Or it is redundant to them.
The .243 doesn't overlap, it BRIDGES. The 243 isn't supposed to be for elk, it is supposed to be for deer...AND it is supposed to be for long range varmint. That one chambering covers a huge swath of game. When it all boils down to it the 6.5x55 is left with one trick. It is the softest recoiling cartridge that can handle elk. Everything else is overlap.