So, I really like the ideas behind PF1 multiclassing; the idea that class levels are like Lego blocks you can combine in a lot of unique ways. However, there's a number of issues with this:
First is how different tracks work, more specifically, there are class-specific tracks vs more universal tracks. Universal tracks are stuff like the saves or Base Attack Bonus; they tends to increase regardless of what class you take levels in. Class-specific tracks are closer to stuff like spellcasting, which only advance when you put levels in specific classes. From how I understand it, classes that rely on universal tracks tends to suffer less from multiclassing, and those that rely on class-specific tracks suffers more.
Next is how front-loaded a lot of class features are. Classes tends to get a lot of features in its first few levels so that the class can be recognizable something specific early on, but this means that the early levels can end up being worth a lot more than the later ones. Players tends to like to get their concept "online" as quickly as possible, so front-loading a bunch of stuff is good for this reason. However, this does also cause a lot of issues with the idea of class levels being interchangeable, combineable, "blocks" if some of these class levels are worth more than others.
As I understand it, the latest version of D&D "fixes" some of these issues by having the class concept not really go online until level… 4 I think? Levels 1-3 is more like training to be a class and can sorta be seen as tutorial levels for newer players, while more experienced players are meant to start later. This helps keep the idea of class levels being mostly interchangeable and combineable in tact, but I can imagine a lot of players not being too happy with this since it means character concepts can take a higher level to go online. This would also generally weaken multiclassing in general. I'm not sure what they did, if anything, about the universal/class-specific tracks issue.
PF2 abandons the idea of classes being like Lego-blocks and instead makes feats do that. This means there is much less distinction between class-specific tracks and universal tracks, as well as allowing them to make powerful level-1s of classes without worry they'll just be pouched for multiclassing purposes.
If I got something wrong, please tell me. I don't really have much in terms of playing experience, so I'm going mostly from what I've read or heard about it.
Each of the solutions have their own pros and cons though, but I do feel PF2's allows for a great amount of diverse character customization without requiring a large amount of systems mastery to make use of.