This really depends on what you want to do...
Flash has more limits, but the project you are doing could most likely
be done in Flash,
and probably faster than in Java...
Not entirely sure how you were thinking of designing it,
but considering it is web based I would expect a web server with a
database (MySQL or Postgresql).
And either using cgi, coldfusion or php on the server side (or jsp and
java enterprise applications(I can never remember the proper name)).
(Coldfusion is probably easy to use with Flash programs considering it
is a Macromedia thing, but I've never used it, so can't say for sure if
there's really any difference between using ColdFusion or something else
for communicating with flash apps)...

However if you are going to do very complicated stuff that requires
real-time networked systems and such, java would probably be a better
choice,
I know this type of stuff has been done with ShockWave, but never heard
of just flash doing real-time networking.
It would require coding a server app to, so it would quickly grow to a
much larger scale production though...

Both requires that you learn some programming, but ActionScript is
basically a slightly more advanced Javascript.
Both should work for what you want to do, but Flash would most likely be
easier,
although I can't be perfectly certain of what you are trying to do.