Both are useful for testing. Neither will tell you whether or not you’ve found a meteorite since there are many other odd-looking rocks and pieces of man-made materials which will respond to one or the other, or both.
They will however help determine possible classes of meteorite for a find that has other encouraging characteristics to suggest it might be a meteorite.
Those with a high native iron content will respond strongly to either type of magnet and the degree of ‘pull’ will help determine the amount of iron… at least on a high/medium/low basis. That can help in determining whether a meteorite is a nickel-iron, a stony iron, a chondrite or a stony achondrite. And if it is a chondrite, whether it’s ‘H’ class or ‘L’ class, or carbonaceous.
If a meteorite responds to a neodymium magnet, but not a fridge magnet (or barely so) then its potential classes are limited to some particular LL chondrites, some carbonaceous chondrites, and many achondrites.
I actually also use an intermediate strength magnet of the kind sold in toyshops for kids and by better stationery stores (and some haberdashers) as helpful way of determining the degree of pull on a comparative basis between the three magnet 'types'.