I find it funny that the creator of Dragonball has said (on the record) that the switch from the original franchise to Dragon Ball: Z was merely a marketing ploy by the production company; it's also funny that the "Z" was chosen to ensure this was the last instalment, given how we now have multiple additional films and the whole DB: Super sequel (not to mention DB: GT, even if that isn't canon). It seems odd because there is such a clear tonal and even artistic jump between the two shows!
When we last saw Goku, he was a teenager. Now he's a full adult, with a wife, a five (I think?) year old kid, and a very different outlook on like. We'd seen the start of this maturation in the Piccolo Jnr. Saga, but right from the first episode of DB: Z it's very clear that this is a fairly different character. He's still carefree and not entirely "civilised", but he's also smart, resourceful, and has a very clear view on morality. This is probably most evident in the saga's finale, when he pleads with Krillin to let Vegeta go, and not to kill him, but the roots of that philosophy are scattered throughout the season.
And it's not just Goku ‒ pretty much all of the characters have aged and matured in their characters (except for Chi-Chi, who has changed considerably in a slightly less than beneficial direction 😅). And the animation and writing style have grown up, too. Gone are the overtly pervy jokes and plot lines; nudity is now "tastefully" hidden, even with child characters like Gohan; and the violence has been toned down considerably. That latter decision has sidelined a few characters (most notably Launch), whilst also calling for redesigns of others, such as the Ox King.
But whilst "real world" violence has been almost entirely removed, the superhero-like abilities of our heroes has been amped up. I'm a bit sad that we don't see this happen directly. Much like the time skip in the final Dragonball saga, this new jump forward serves the plot and character development well, but also means that we just have to accept a lot of new capabilities and super-human skills from everyone. Flight is the most obvious sudden addition! In the first series, a select few fighters could hover or hold themselves in the air, whilst most could jump really, really high, OG Superman style. But no one was ever shown with the power of fully manoeuvrable flight. Now, even Gohan has that capability, no explanation provided. Similarly, whilst we did see some energy attacks and energy-based power-ups were hinted at, the kind of energy-overdrive that Goku unlocks during his time with King Kai is just added in there. Yes, we get a lengthy, multi-episode training montage, but the actual bit where Goku is taught the Kaio-ken technique happens off-screen 🤷♀️
One area of development I'm really happy to see they didn't just hand-wave away was Piccolo's conversion from foe to friend. His team up with Goku to attack Raditz makes clear sense once he's realised how powerful the new Saiyan is (his ability to sense power levels is glossed over a little, but ah well). Then, learning that this was merely a scout (of sorts), his choice to train Gohan, who has just shown extraordinary potential, also feels justified, and provides him an obvious arc to begin to care about this kid and, by extension, the other Z fighters. (Oh yeah, the whole "Z fighters" thing is also never explained, apparently, they just suddenly start using it 😂)
None of this would matter, though, if the Saiyan Saga wasn't such a good bridge arc. It cleverly weaves in a bunch of revelations about Goku and Piccolo's origins, introduces us to a wider universe of threats and potential allies, and sets the stage for a much grander story, both in terms of the inevitable trip to Namek, and also the interconnectedness of the core characters. Plus, killing off a bunch of the fighters does also help narrow the scope of play a little, which is definitely beneficial too. I do wish Raditz and Nappa were a little less one-dimensional, and that Vegeta wasn't so absolutely evil, but I'm also impressed at how much of his future characterisation is subtly present here this early on.
The result is a really solid chapter in the ongoing narrative, and an excellent introduction to this new version of the classic show. It's still a little slow at times, and there are a few moments where you're left thinking "why wouldn't you just do X or Y?" (particularly around the lack of sensu beans ‒ come on Korin, you had a few years to grow a good stock!), but the setup is intriguing, the extended training middle section is really good fun (I thoroughly enjoyed Goku's time in the after life), and the final battle is surprisingly impactful and nicely balanced (aside from the whole "Vegeta powering up is felt all over the globe", when in later seasons they exceed that power level a hundred fold multiple times without it registering outside the battlefield at all 😅), which rounds it all together well.