I'm very familiar with 3.5, somewhat familiar with PF, but only know the core ruleset of 4e. Nevertheless, since no one else has answered, I thought I might as well take a stab at the major differences. I'd say the general theme is that PF offers more paths while building a character, at the cost of offering more dead ends as well. Similarly, monsters are more flexible, but more difficult for the DM to run.
I think you could write an interesting essay talking more about the philosophical and design differences between the two systems, but in answering this question it'll be more useful to address the observable differences point by point.
Class and monster roles
Fourth edition (4e) has clearly defined class and monster roles. This isn't the case at all in Pathfinder (PF). A fighter in PF might be good at dealing damage (striker) or a great tank (defender) but this will depend entirely on how you build your character. Monsters do not provide an obvious indication of how they should be used; the DM has to examine their abilities and think about what their role should be in battle.
It's very easy to build an ineffective character in PF, as a consequence of the greater flexibility you have in defining your role.
Multiclassing
Since in PF each class defines its own progression, every time a PC gains a level they can choose what class to advance in. Again, this means it is possible to design a character that performs very poorly. It would be a bit like creating a 4e character that drew from multiple classes, but was capable of using only heroic level powers while everyone else was choosing a paragon path.
Paths vs. Prestige Classes
In 4e, there are three distinct tiers of play, and you can choose a paragon path and epic destiny as you progress.
There's no direct analogue to the tiers in PF. The closest thing to a paragon path is a prestige class -- a class that can only be taken when you meet certain requirements. This was more of a big deal in 3.5, where it was used for character customization; in PF there are many fewer prestige classes, though they might be important for certain multiclass combinations.
Defenses v. Saves
This is purely technical, but confusing if you're not expecting it. Defenses in 4e are equivalent to saving throws in PF. If a wizard casts a spell, rather than rolling an attack, the defender rolls a saving throw against a DC set by the spell.
Automatic progressions
In 4e, you add half your level to a great many statistics. PF is not quite so straightforward -- your class(es) will determine your base attack bonus and saving throw progression, and you must pick how your skills improve every level. Other abilities like AC or initiative do not naturally increase as you level.
Powers, Spells, and Maneuvers
This is probably the most fundamental difference from a player's perspective.
In 4e, every class has a list of powers they can learn as they level. These powers are divided into at-will, daily, and encounter powers that dictate how often they can be used. Pretty much any special ability a player has is derived from a power -- and those powers are chiefly geared towards combat. Casting classes can gain rituals which are less combat related, and work off a different economy than combat powers.
In Pathfinder, it works a little differently. Casting classes have spells, which are probably closest in spirit to 4e powers, but tend to be more flexible. The number of spells you can choose from is quite large, and different classes have different mechanics for learning and casting these spells. Spells useful in combat consume exactly the same resources as more role-playing oriented spells.
Meanwhile, melee classes rarely have the same type of limited powers. Anyone can push, grab, pull, grapple, trip or disarm a foe during combat, and you can do so as often as you like. Doing so means sacrificing damage, though; you will only do damage with a regular attack. Unlike 4e, forced movement is quite difficult to pull off in PF, which is why a grid isn't as necessary.
As an example, a fighter in PF progresses chiefly because they get better at what they've been capable of doing all along, rather than getting spectacular new powers.
Monsters
This is a big difference from the DM's POV especially.
In addition to fitting certain roles (as mentioned above) monsters in 4e are often defined by a set of bespoke abilities. In contrast, monsters in PF always play by the same rules as the players. Their hp, attacks, saves, and skills are defined and limited by the type and HD of the monster. The majority of unique special abilities are copies of spells, or one of a small set of abilities common to many monsters. Often a powerful monster will have a large set of abilities they will never use in combat, but can provide role playing hooks.
There is no PF equivalent to elite or solo monsters -- you simply must use a higher level beast to provide a greater challenge to the party.
Overall the 4e system is much easier on the DM in creating encounters. For those so inclined, though, the PF system allows the creation of some interesting beasts; you can even add class levels to monsters, much like PCs can multiclass.
Magic items
The majority of magic items in PF do one of two things -- they either increase the attributes of a PC, or they can replicate the effects of spells. Magic weapons and armor combine several different attributes, almost Diablo style. Compared to the 4e items in core, they are much more varied, and what specific item your character has can drastically affect what they can do. The downside is that it becomes harder for a player to choose the 'correct' gear.
Best Answer
D&D 5e has been optimized to make it simple to learn and play, which is what you are reacting to. Its design reflects the fracturing of the D&D fanbase after 4e, and to a certain extent embraces a more “old-school” (read: 2e or earlier) playstyle in which the rules are much more nebulous, fluid, and handled ad hoc by the DM. This both makes it simpler to learn and play (since there aren’t rules to learn, you just have to trust the DM’s judgment), and also mollifies some of the critics of 4e (and, to an extent, 3e) in an effort to reunite the fanbase.
The downside of this is that more of the experience is riding on the DM’s expertise and judgment, and the players are often not left with a lot of surety in terms of how things will work from one DM to another. That makes it difficult to plan on things as a player, and can in some cases reduce player agency.
Pathfinder 1e was a spin-off of D&D 3.5e, and is for the most part identical in its foundations to that system.1 D&D 3.5e was likely never intended to be, but in some ways it was a departure from 2e when it comes to the subject of “rules vs. rulings,” as the more precise language gave many readers the basic assumption that things would generally go mostly by the rules and that exceptions would be, well, exceptional. Pathfinder inherited this heritage, though Paizo tried to repudiate it, and despite the fact that, like 5e, Pathfinder was in large part a reaction against D&D 4e, which was the system that most truly embraced the “rules” side of “rules vs. rulings.”
With Pathfinder 2e, Paizo has seemed to, at least somewhat, more fully embrace this “rules over rulings” ethos, in a way they largely didn’t with Pathfinder. And, in ways that are probably not coincidental but I’m not sure were planned, Pathfinder 2e is actually reminiscent of D&D 4e. The lists of class feats feel very similar to 4e’s lists of powers for each class, and the use of tags is very similar to 4e. Even the design and layout of the book feels like 4e—the little action diamonds just look like 4e’s heavy usage of the ♦ character in power descriptions, and the nature of the one-two-or-three diamonds is similar to 4e’s color coding by power availability (at-will, encounter, daily).
Paizo has also discussed PF 2e in these terms, describing their audience as being more technically-minded, more interested in the rules themselves, as being interested in digging into them and combining them in creative ways. It would seem that these appearances are not merely superficial, and possibly unlike Pathfinder 1e, not unintentional.
The long and short of it is, yes, it is fairly likely that Pathfinder 2e is at least intended to cater more to your tastes than D&D 5e is. You may also want to take a look at D&D 4e—which, as I mentioned, probably wins overall in “rules over rulings,” even more so than Pathfinder 2e.