No, Civ 4 isn't more cartoony than Civ 6. Graphic of Civ 4 just isn't realistic enough, and that is largely due to the limitation of graphical technoloy of 2005, not due to the art design of Civ 4.
Civ4's "not realistic enough" doesn't mean it is cartoony, you can see that unit models in civ 4 still have realistic proportion, they just doesn't have enough details. While in Civ 6, the some body parts (like hands, arms) of units are overly exagerrated, that's what we call "cartoony" (and what the devs called "stylized").
When it comes to unit models, like for example the warrior in Civ 4, I think you are correct in saying it could be described as cartoony (the same goes for the 'pow' visual effects), among many other things. Cartoony, and stylised, can be used interchangeably here, as cartoony is a form of stylization.
However, to say that by definition Civ 4 was less cartoony because it simply couldn't be more realistic for its time is nonsense. You can clearly see from
the leader portraits (also shown below) that they were cartoony. In fact, I would argue that if Civ 4 had the computational power (or graphical technology) it would like almost identical to what we have now; the direct modern equivalent of its leader portraits is what we have now in Civ 6, as Civ 4 contains the same extreme facial features at times (wide and wide-set eyes, large cheeks and ears, among other things), with some leaders looking more realistic and others less so, which can easily be argued to have a similar art design to Civ 6.
Furthermore, to counter the argument that a more realistic portrait was not possible, one simply needs to look at Red Alert, which came out ten years prior, in which Stalin can easily be seen
with extremely realistic graphics (also shown below), or at Stronghold 2 which came out the same year, showing leaders with graphics of that time
that look far more realistic (timestamped link to YouTube) than Civ 4 leaders. As the examples linked show, had the developers wanted to go for realism, they could have simply hired actors like they did in Red Alert, or animated more realistic looking humans like they did in Stronghold 2. So to simply state it was not art direction, but simply the limit of technology, is misleading, as it was definitely the case that they could not go for photo realistic animations, but also definitely the case that there was a strong art direction for the leaders in Civ 4.
In the end, I think most people that dislike Civ 6 graphics want to argue Civ has never been goofy or cartoony, and lean on selective arguments from earlier games, to validate their argument and therefore their opinion (which is entirely unnecessary, any opinion on the looks of the graphics is entirely valid). It is true that the units in Civ 4 were less cartoony looking than in Civ 6. It is also true that the leaders in Civ 5 were less cartoony looking than in Civ 6. Sillyness, whether it be graphical or otherwise, has always been a part of the Civilization franchise, whether it's the leader models for Civ 4 (Hatshepsut I'm looking at you), or the cartoonesque advisors in Civilization 2.
Everyone is entitled to their own opinion. Civ 6 might be too cartoony-looking for you (indefinite 'you', not zwei833 in particular), but to state it's all new to the franchise, or that previous Civ titles had to look that way because of graphical limitations, is simply false. All Civilization entries had art direction, and Civ 5 and 6 had the clearest, most cohesive art direction of them all. Personally, I like the graphical style of Civ 6 as it is timeless. However, I can easily imagine how those might feel that do not care for this style, as 6 has done a bang-up job of keeping all graphics (UI, models, units, terrain, menus, etc) in one cohesive style, making it a pain to look at if you do not care for it particularly.
https://i.imgur.com/i2aUHpH.jpeg
Just read his own description of the mod:
