Moving a database between 5.0 and 5.1

Hi,

I have a large database running on MySQL 5.0.45.

I want to test my application with MySQL 5.1, but I don't want to
overwrite my 5.0 installation just yet. So I installed 5.1 in a
different directory and assigned it a different port number.

It's my understanding that I should be able to copy my database onto
the new server simply by copying its subdirectory from the 5.0
server's data folder into the 5.1 server. However, this does not work.
When I start MySQL 5.1 after doing so, it shows the database but
crashes when trying to query it. If I run mysqlcheck, it reports that
every table is corrupt and says the reason is "Can't find file". (All
the files are there).

I also tried copying the entire data directory (not just the one
database) but got the same error.

I realize that I could backup my database with mysqldump and restore
it, but the database is huge and the last time I had to do this, it
took 9 hours to restore.

Am I doing something wrong here, or should I be able to move databases
around like this?

Thanks,
Frank