I came into the game late BC. I think the Zul'aman patch was one of the earlier things I remember.
By the time I got into heroics, the majority of them were be roflstomped by people who completely overgeared the instance. People didn't want a warrior tank, because then they couldn't put up blessing of salvation, and aoe their way through the place. There were exceptions, Magisters and SLabs, and Halls seemed to scare people a bit.

Which comes to the next difference. I basically played just my warrior at 70. Getting a group as a non-cc dps'r for certain heroics was nearly impossible. To the extent of forcing me to become a tank because at least then I could get some groups. CC was important, trash was scarier.

However, by the end of the expansion, people knew the pulls, cc'd their crap, range pulled, overgeared, and cleared with relative ease.

As for us being better, and the overall gap: What we have learned now, is a different set of tools. The skill now is how to dance, how to maintain uptime/numbers, how to gear. We dodge ten times the number of mechanics as we did back then, but apparently such dodging is easier, especially with all the warnings and third-party boss mods. In BC it felt like management of one's resources was much bigger. Whether it was mana, defensive cooldowns, cc, agro, etc. Fights were more standstill, but we had less class tools and personal resources to use. I think the difference is that that kind of premeditation of abilities is harder than reactively dodging out of the puddle on the ground.

That's my take on it anyway.