Personally, TNG made an indelible mark on me, but then I was 17 when it started so I was still "impressionable" at that age, especially when a show like that affected my artistic development as a writer. Tasha Yar actually actually made the biggest impression on me at first--imagine being a 17-year old girl and seeing a female chief of security for the first time, in a time when women were actually gaining and holding equality in the workplace. It was my first tangible exposure to Girl Power as a young adult. (Well, that, and I was thinking about this the other day: I remember an episode of TOS where Uhura had on a pair of coveralls and was actually under a console fixing something, and I remembered thinking as a little kid that this made her really smart and badass!

) That, and for the late 80s, that hairdo was really rockin', and it was the reason I finally got my mom to cave and let me start coloring my hair--so I guess we may have Denise Crosby to thank for my career choice! Any way, each individual character made impressions on me, some I liked better than others, and some dynamics I enjoyed more than others (ie I got more into Picard/Crusher than I did Worf/Troi...running the risk of blasphemy here, W/T was just "Really? Are you kidding me right now?" for me.)
The lack of a Big Three type friendship was, I think, because they really did try to do something different with TNG and make it truly an ensemble cast, with no character being (that much) more important than another. You actually got a Geordi episode here, a Worf episode there, a Troi episode later on...with TOS, you had Kirk, Spock, McCoy, and sometimes Scotty, and the rest were written in such a way that they were just there when you needed someone else to say lines. That's how television was done at the time. Nobody was really doing ensemble cast shows back then. Plus TNG was groundbreaking in that meaningful romance was even hinted at let alone delivered (though I still don't dig the Worf/Troi thing) in a Star Trek show, versus the occasional "Wham, bam, thank you, Alien Ma'am."
So I guess to me I would just say that I loved each just as much, just differently. Cliche, I know, but it really is apples and oranges to me.