I have sentimental/nostalgic reasons for picking the Saiyan Saga/Vegeta Saga as my favorite.
I have to pretty much write a biography to explain though.
Growing up between ages 9-12, I had a friend a year younger than me that was keeping up with DBZ as it was unfolding in the USA and airing on Toonami. I wasn't that interested at the time, but I occasionally talked to him about what was going on at the time of the show while we played with his DBZ figurines. Talking about who was the strongest at any given time. I remember being confused, because every time I'd talk to him he'd say someone else was the strongest

.
When I was 16, we finally got cable TV and they ran a re-run of the Ocean dub on Toonami again during my summer break. I remember watching something else and seeing an ad saying something like "Tune in at so&so time on such day to catch Dragon Ball Z re-aired for the first time since blahblah starting soon". I don't remember what it actually said, I just knew it was my chance to actually watch it start to finish. It aired at 10:30 PM every Thursday I think.
So I watched the entire Saiyan Saga that way. I got hooked and obsessed. I even remember arguing with my dad a few times in attempts to not miss an episode. He wanted me to go do this or that and I'm like, no, I wanna be free Thursday for DBZ!
Something about watching the Saiyan Saga one episode per week REALLY has you on the edge of your seat. It was exhilarating.
I remember we had a "middle-room" in our trailer, where my brother & I kept our stereo, guitars, TV, games etc. Basically, we had a bedroom, then we had an activity room. That was the year that my brother moved out, so I had that room all to myself for the first time. I remember creating this sort of comfortable cradle of pillows & blankets on the floor before watching every episode. I'd turn the lights out and it was just me and DBZ.
But once it reached the Frieza saga, the whole space travel thing seemed ridiculous to me. In a close-minded fit, I stopped watching after the episode where they ran into the space ship full of kids.
It wasn't until a couple years later that I discovered the now-defunct DBZ.TV website streaming every episode and every movie, including GT. I watched all of it. I re-watched the Saiyan Saga, all the rest of Z, all of GT, and every movie at the time. It felt like an accomplishment.
Since then, I've probably watched every saga at least 6 times over.
But I think the experience of watching the Saiyan Saga on TV weekly in anticipation offered an experience much different than binging the series all at once. I just remember it differently. Now when I watch anything from that saga, I still remember what it was like to be 16 year old me, on the edge of my seat, in my comfy spot, with the lights off in that room... watching Nappa beat the piss out of everyone.
