(Disclaimer: Every cat doesn't adhere to breed standards. It's a good
guideline, and indicator of personality, but not a guarantee)
That said, Maine Coons are for the most part very gentle. Speaking for my
daughter's two, they seem to be a bit timid around children, but then, she
doesn't have any. It would probably be a different story had they been raised
with children. To my knowledge, they have never bitten or scratched anyone,
ever. They are very laid-back.

Sherry

It all depends on the individual cat, the kids, and the situation.
Most cats will scratch and bite if that seems necessary. Some cats
will attack for fun with various levels of damage possible.  Most kids
need instruction on the human behaviors appropriate for cats and other
pets. Some kids learn well. Others do not.

If young kids are involved, you would want to play close attention to
keeping cat claws blunted or covered.

If you have time and patience needed to instruct yourself and your
kids on feline-human relations, I'd say go for it. Kids and cats can
have great fun.  Otherwise, do yourself, the kids, and the cats a
favor and pass.  The combination of kids, cats, and too-busy parents
can lead to disaster for the cats and unhappiness for the humans.

Maine Coons, in my limited experience based on just a few individuals,
tend to adapt relatively well to new situations. They are, however,
large, strong, playful, and capable of defending themselves if
necessary.

Ragdolls are usually very good with children. They often tolerate being
dressed up. They get their name because the often go limp like a ragdoll
when picked up. If you're considering a purebred check out the breeder. Find
out how she socializes the cats. Some breeders have beautiful cats, but
don't handle them when young so they are shy with people.