Gonna keep it short and simple 
fx100 is my go-to calculator, firstly the numbers are much bigger + easier to read (although more pixelated) than the new one.
it gives answers in decimals, which then you can convert to fractions with the S<=>D button in one click.
fx8200 gives answers in fractions, you'll need to press format>decimal to change, which you'll find yourself doing A LOT.
New calc can give answers in surds like sin(45) -> sqr(2)/2 which the old cannot.
also allows input for different log bases, unlike the old one where u need to use a change of base formula.
The case for the fx100 slides on and off, pretty good for the first few years until the sides start to chip and the lid completely doesn't attach properly.
New case uses a top and bottom clip, kinda clunky but should last longer than old calc.
Perms+combs+factorials are in the catalogue function for f8200, making u press 6 buttons just for a C.
old calc is a simple one click of a button, much more efficient.
tl;dr:
fx100 good but lacking some stuff
fx8200 more functions but dumb design
fx100 is my go-to calculator, firstly the numbers are much bigger + easier to read (although more pixelated) than the new one.
it gives answers in decimals, which then you can convert to fractions with the S<=>D button in one click.
fx8200 gives answers in fractions, you'll need to press format>decimal to change, which you'll find yourself doing A LOT.
New calc can give answers in surds like sin(45) -> sqr(2)/2 which the old cannot.
also allows input for different log bases, unlike the old one where u need to use a change of base formula.
The case for the fx100 slides on and off, pretty good for the first few years until the sides start to chip and the lid completely doesn't attach properly.
New case uses a top and bottom clip, kinda clunky but should last longer than old calc.
Perms+combs+factorials are in the catalogue function for f8200, making u press 6 buttons just for a C.
old calc is a simple one click of a button, much more efficient.
tl;dr:
fx100 good but lacking some stuff
fx8200 more functions but dumb design