What does the alnico IV do to it vs the alnico V?
Magnet swaps change your tone relative to the magnet you had before, i.e., not all A5 or A4 pups sound the same, but swapping an A5 for an A4 should adjust the EQ on the pickup similarly regardless of how you started out.
When you swap from an A5 to an A4, you will get more mids, lose some treble, lose some bass, and get a "spongier" feel to the bass that you have (i.e., less "tight," more "sag," - more of a "liquid lead tone" if you were doing quick single note lines with gain, or less "spank" and attack if you're playing clean). A4 will also be lower output a little bit (not usually a problem for most players when we're talking about a neck pickup).
I've had a '59 neck, and from favorite to least favorite, I liked A3>A4>A5>UOA5. I like less bass out of a neck pickup than most people, so I wouldn't be surprised if more folks preferred the A4 over the A3.
Anyway, I can definitely get behind JamesPaul's suggestion - an A4 '59 neck is a beautiful thing