I wasn't around for the original series but I loved the shit out of TNG. I don't think anything has since quite captured the sheer awe and adventure of those shows, apart from perhaps SG-1.
I also missed the original series and loved TNG and even enjoyed Voyager. Tried rewatching the original series on DSTV but just found it a bit too cheesy for my taste. The fist 4-6 seasons of SG-1 is close yeah but like alot of stuff it just got stupidly melodramatic in the later season. I enjoyed Atlantis as well but it had the same issue, got stupid by season 6.
Yeah once they get into 'saving the world/galaxy/universe' mode things get silly. I liked the exploring and discovering strange new places and beings.