I am presently on my first watch through of VOY and I'm about to start the fifth season. Thinking back to very early episodes of TNG and early episodes of VOY i will concede VOY had better crew interactions and they were much friendlier towards one another.
That might be partially do to TNG being a relaunch of a TV series cancelled 18 years ago, while VOY was launched during Trek's height of popularity with familiar production and writing staff. However mostly i think it comes from the VOY crew being acquainted with one another prior to forming the "one crew" we see at the end of Caretaker.
Chakotay is BFF with B'Elanna
Janeway is BFF's with Tuvok
Harry and Tom became friends fast after meeting
Kes had Neelix and was kind to the Doctor before he developed a personality
Janeway had broken Tom out prison and was friendly enough with him that by the third episode he was volunteering to help her on things he wasn't qualified for.
Tom and Chakotay had a history in the Maqui.
What can we say about TNG?
Picard was and old friend of the family to Beverly and Wesley.
Riker and Troi used to date.
Had TNG started with Data and Geordi being BFF's
Worf and Riker being BFF's and willing to kill for one another
Troi and Beverly being close friends like they were in later seasons
Or even Picard being a closer mentor to Tasha. We could've seen something as similar to VOY in the early days of TNG. Keep in mind DS9 wasn't a well jelled crew either at the start. I could list them out but won't.
Outside of that when you start to peel back the onion of each crew. You find the TNG characters to be more likable and believable.