Swapping magnets does effect perceived output, but it is more useful for tone shaping. Each grade of magnet has different tonal characteristics that you can use to shape the pickups tone. You haven't mentioned if it's the bridge or neck pickup or the Ohms output of said so my reply may seem a little and long winded.
Alnico 2 magnets are the 2nd lowest strength magnet in the Alnico range which results in fantastic vintage dynamics and flavour. This magnet can be used in either position (Bridge or Neck) but is best used as a bridge pickup magnet where you tend to get a brighter and tighter tone naturally – the warm Alnico 2 helps tame the bite a bit. An Alnico 2 magnet will tend to get mushy and dark sounding in a neck position humbucker. This is one of my favourite bridge position magnets.
Alnico 3, the lowest in strength of Alnico magnets, is similar to the Alnico 2 but tends to generate more treble, slightly scooped mids and a softer-yet-tighter low end. This is my favourite magnet for a neck position humbucker, especially when looking for that aged PAF tone. An Alnico 3 humbucker in the neck position typically has a flute-like woody tone with plenty of clarity and allows the guitar’s character to come through quite nicely – I’ve personally noticed a P90-ish type of tone when used in the neck position. It works excellent as a bridge humbucker magnet as well when you’re looking for that vintage PAF tone on the cleaner side. This magnet in the bridge position can beef right up with slightly overwound coils for a warm compressed rock tone with a bit less edge than an Alnico 2 yet retain some shimmer on top giving a fairly 3D quality to the tone.
Alnico 4 magnets generate a flatter “EQ” overall which can sometimes sound bland to some players, yet have been the hidden little secret for others. This magnet tends to sit between the Alnico 2 and Alnico 5 in magnetic strength and tone – rounder lows than a 5, tighter lows than a 2 with crisper highs than a 2. With the ALnico 4’s flatter “EQ”, the guitar’s true colour and character really shine through – this is where Alnico 4’s can sometimes sound bland. Some guitars just simply don’t work with Alnico 4 magnets, but when a guitar works with Alnico 4 it’s pure PAF magic. In my personal opinion, these magnets work best in a naturally big-sounding guitars.
Alnico 5 is the strongest of the most commonly used magnets and has been a very popular choice of magnet. Being the stronger magnet in the range, it tends to generate more output, tighter low end, scooped mids and sharper treble bite. These work great in a low-wind neck pickup for very crisp tone. When in a hotter neck pickup, the Alnico 5 may lean towards the boomy side which can overpower the highs. In a bridge humbucker, the Alnico 5 will work best in a hotter wound pickup where you’d want to bring in more low end and shave off the highs to tame the bite and avoid the dreaded ice-pick-to-the-ear-drum. In a lower wind bridge humbucker, the Alnico 5 may sound thin and brittle compared to an Alnico 2 or 4.
Unoriented magnets like UOA5's are a great alternative for 2's and in geneeral when talking about vintage PAF this is is the magnet often referenced as a A5 magnet. Both magnets are the same strength but the way the magnets are made differs. Standard magnets go through a process that lines up the magnet molecules North to South whereas ALL UNORIENTED magnets skip this part of manufactor so the molecules are random and haphazard in the magnets structure. This causes the magnet to sound a little smoother in the treble and rounder in the bass than their oriented alternative. The manufacturing proccess is cheaper for Un-Oriented magnets and so Gibson would of sourced these over oriented ones.
While there are unoriented version of most magnets available I personally only use UOA5's.
Two relative newcomers on the market are Alnico 6 and Alnico 8. Both of these magnets are like A5's on steroids and work great replacing ceramic magnets in high wind pickups.