Is Bitcoin database cross platform compatible?
It should be compatible if your running one instance at a time, BUT I think that the datadir is being locked. 
Try to find more details in the logs, it should tell you the reason of the error which could be anything.
if you are running any bitcoin software on windows stop it and try to restart bitcoind from your linux box. 

EDIT: Did you install bitcoind and run it as root? if not, can you try to chown -R  ~/.bitcoin as root, not the db folder itself, it still can be a permission issue,