I think the only major difference between the typical P2/P3 chipsets regarding RAM is that the older 440bx can handle up to 8 logical "rows" (sides) of 128MB each, but the i810/i815 are limited to 4 sides of 128MB each, which is why it maxes out at 512MB. Usually those boards only have 2 memory slots to eliminate confusion about it.
A double sided and "unbuffered" 256MB module which uses the "16Mx8" chip types would be correct for these chipsets and should most likely work. Unfortunately it's not easy to find out what chip types are being used until you have the thing in your hands. If you stick to reputable brands then you can safely assume that any PC133, double sided, 8 chip per side, 256MB module should be good though. As far as I know the only double sided 16-chip modules that still have incompatible chips are generic no name stuff.
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If it's 256MB PC133 double sided, with 16 major chips, 8 on each side (not 9), and branded by somebody like Kingston, Micron, Crucial, Corsair, etc. then it should be fine. Sticking to good brands reduces the number of ways you can get fooled.