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(Disclaimer: I'm Polish, so English is my second language, and this is my first post here, as far as I know. Also, I don't grasp the probability curves involved in most of the discussion here, so any feedback on that will be appreciated.)

Okay, I'll bite into the topics, but it will go against the usual D&D weapon moulds. Realism issues and real life archery info was already discussed here, but...

You might have noticed, that there are three types of crossbows: a hand crossbow, a regular crossbow and a heavy crossbow. Why not apply the same classification to bows, to get a more realistic and rules-savvy system?

First, we get the >Shortbow. It stays the same, a 60-ft. range, 1d6 piercing damage weapon with deadly 1d10.
For realism purposes, those are small hunting bows, usually below 1 meter of height, and quite small pull (tension strength? I don't know the proper English term for that). They were used to hunt birds and small game animals, like rabbits, and were mostly used by commoners, and almost never in regular warfare.
On the other hand, the composite shortbow is a different animal altogether. It's the same size, or even smaller as a regular shortbow, so it's use is similar, but the materials are radically different wood laminates, cartilage, and bone (mostly*). That gives them both a disproportional stopping power (for their size), and makes them a great cavalry weapon. Think middle-eastern and eastern cavalry, for example, the Tatar and Mongol people were masters of mounted composite shortbow archery.
So, a >Composite Shortbow would be a 90-ft. range, 1d6 piercing damage weapon with deadly 1d10 and propulsive.
The change in range is to show how much a composite bow is stronger than the regular one, and that easily converts into effective weapon range. Most experts give composite bows half as much power as a regular one of the same size.

Second, we have the bow. The regular one, that's so often mistaken for a longbow in fantasy settings. There's a difference, but let's leave that for later. It's usually slightly shorter in height than the user (at least to the sternum, but mostly up to his chin), and has a significantly better power than the shortbow, even composite(but a range on par with a composite one).
The >Bow would be a 90-ft. range, 1d8 piercing weapon with deadly 1d10. No changes. besides the range, so that composite shortbow users can't effectively outrage regular bows.
So again, a >Composite Bow would be a 120-ft, 1d8 piercing damage weapon with deadly 1d10 and propulsive.
A change in range again, but we have diminishing returns here, because a part of the composite features are curvature, that makes them even smaller (~10-20% less than the length of a regular bow).

Third, we have the longbow. Not just a bow, but a real monster. It has power, that most people can't even tame. It's way too hard to use if you're not a tall, muscular person with one arm significantly more developed though years of training. It's taller than you are, with a length of around 2 meters (6 ft. 2 in.), and can't be really fired in rapid succession. It would kill your arm to do so. They tended to have 100 to 180 pounds of draw strength. That's roughly 45 to 80 kilograms. they would be longer than the average height of even a tall person.
But that doesn't mean you couldn't shoot people up close, since at short ranges it would work like a crossbow, with an almost flat trajectory. That means we need something to simulate it's real-life properties in PF2, and not make it outstrip the heavy crossbow. So...
The >Longbow would be a 120-ft. range 1d10 piercing damage weapon with deadly 1d10, propulsive, and volley.
Where >Volley means that the weapon in question is hard and very exhausting to operate. A second attack with this weapon imposes a -6 penalty, and a third one a -12 (so, the opposite of Agile).
Optionally, beyond making a >Longbow a Exotic weapon, there are two additional effects I would consider, but they're probably too complicated, and too much of a penalty.
1. A critical failure result while attacking with this weapon makes you >Sluggish 1, as the resulting strain to your muscles causes you to yelp in pain and forces you to cower and flex them. If you critically fail an attack with this weapon while still >Sluggish 1 from a previous failure, you become >Fatigued 1 in addition to increasing your >Sluggish condition.
2. Unwieldy: This weapon needs a significant amount of space to use freely, and imposes a -2 penalty to attacks if there are less than three adjacent squares free and unoccupied**, or if there are hostile creatures in adjacent squares.

This is what I came up on a short notice, without any testing, so constructive criticism would be more than welcome. As I wrote at the beginning, the numbers need crunching, and my math skills aren't up to speed for that.

* Though there are oriental composite shortbows made of Damascus steel, one of them, a collapsible version, is displayed in the Malbork Castle Musueum in Poland. That's where I work as a tour guide, and had contact with both types of weapons in historical reenactments and museum pieces alike. If you wish, I can provide photos of the composite bows from our oriental weapons collection display.
** So no easy shooting in dungeon corridors or in a tight party formation. A 2-meter bow is really tough to work with in confined spaces.