The only thing I miss about the old days is the 6-man group. There was nothing fun about waiting hours for that perfect combo of jobs/levels to show up so a group could be made, but after the group was assembled, it was usually great. I made a lot of friends in exp groups (most of them temporary, but we had fun) when it was only 6 of us. Working together, pushing our limits, finding our groove... that was great stuff. I still see people running around Jeuno that I remember leveling with back in Crawlers Nest, the Jungles, $hitadel, etc. I can't name one player that I've leveled with in Abyssea.
I can't speak to the challenge of HNMs. Only every showed up to Behemoth once, and we didn't get claim. Based on the community outcry, I can imagine the challenging fights are sorely missed. I hope they do introduce some really tough fights (note: tough fights, not tough claims).