As long as I have a reasonably strong password is it likely someone who knows my e-mail address would be able to hack it?
It looks like your password is completely irrelevant: Dropbox has, in the past (such a widely publicized incident happened on 2011-06-19, official Dropbox response here), accepted any password as valid, for an extended period of time - that is, anyone could have logged in as you, only knowing your username.
This, in addition to the recent change in security policy (which says, essentially, "we can access your files now, despite our previous statements to the contrary"), means one thing:
NO, it's not any safer than having those files publicly accessible: I can't find any kind of guarantee that a similarly massive problem won't happen again tomorrow, and the architecture of the system doesn't seem to protect your files by itself (and relying on external protection, such as
if(password_ok = 1) gets you, uh, free access for anyone).
In other words: there apparently isn't any useful encryption in place (despite previous claims), therefore you should treat the files as if they were out in the open. So, if you plan to store anything sensitive there, don't store it unencrypted: use some external system of encryption (e.g. a Truecrypt container file - even Dropbox's wiki suggests using that [sic!]), and sync the container - it's encrypted on your side, and thus unreadable without your container password (which Dropbox doesn't have); or use a different cloud sync provider which provides actual client-side encryption.