I think maybe some of your phrasing here needs dissecting – like, calling one of two groups “more cartoon” is an extremely vague way of comparing them when both of them objectively are cartoons. I would understand “more cartoonish” to mean something along the lines of… probably more zany, more “out there,” less naturalistic, and I honestly don’t think that would be a remotely fair assessment. Voltorb and Electrode, I think, are some of the most cartoonish Pokémon of any generation. But maybe we’re understanding the words differently.
As for feeling like they’re from a different franchise… well, personally the only Pokémon that I’ve ever felt that about is Genesect, and I suspect other people’s assessments would vary. I suspect it would be helpful to compare some groups of cartoon creatures that actually are from different franchises – say, Digimon. And I think if you look at it that way, in most cases it’s pretty obvious that the Pokémon are much closer to each other than they are to anything from the other group. I am not by any stretch of the imagination an artist or art critic, and dissecting the qualities of different art styles is not really a particular skill of mine, but some things do leap out. Digimon designs are noticeably more naturalistic in their depictions of anatomy, but also much more comfortable including non-anatomical features (armour, weapons, implants, etc). Many of them revel in the potential gruesomeness of their animal inspirations where Pokémon would anthropomorphise it away. They also tend to be extremely detailed. Compare Ariados and Dokugumon. The style of most Pokémon designs clearly has changed a lot over the past 20 years, but I don’t think the magnitude of those changes comes even close to the differences you can observe between two franchises that are, after all, very similar in concept.
Having said all that, again it’s obvious that Pokémon’s style has evolved over time too – and seeing as Pokémon has been around for 20 years now, frankly I’d be stunned if that weren’t the case. Mostly I think the trends that I can see boil down to the newer Pokémon having more detail; there are fewer and smaller areas of block colour, more elaborate patterns, and generally more colours on a single Pokémon. I saw a piece of fan art a few years ago that I think illustrates the differences quite nicely. And actually, I kind of wonder if those differences are artefacts of the differing graphical capabilities of the successive generations of Nintendo handheld platforms. The original black and white Gameboy couldn’t show different colours at all. They didn’t create designs like the ones we have today because the games simply wouldn’t have been able to do them justice. Even in the second generation games on the Gameboy Colour, the number of colours allowed in a single sprite is sharply limited (the game can remember, I think, four colours per sprite, two of which are always black and white), so detail has to be carefully rationed (you can see, for instance, that Starmie’s jewel is purple rather than red, because Starmie’s body is also purple and that keeps your palette to a manageable size; Staryu reuses the red from its jewel as shading on its body). Obviously you can’t prove that this is what happened without quizzing Game Freak about it, but I think the changes in style we observe from generation III onward are more or less consistent with the artists being told “okay, the games can now actually show pretty much everything you draw.”