「だらけ」 has the connotation of being "all over the place" or being "riddled with" . The speaker that chooses this word wants to imply that he's not happy that there's so much of .
This has the idea of "There's nothin' but friggin' dudes up in this place!" i.e. "sausagefest"
「ばかり」 can be simply thought of as "only" in kind of a neutral way where no real preference for more or less being stated by the speaker.
This has more of a "Oh well, I guess there's nothing but men here." sort of a sound to it.
On a side-note you can emphasize that there's ONLY men by saying the following.
Now since we're putting some oomph into 「ばかり」 with the addition of 「っ」it sounds somewhat negative, but it's more like the speaker is expressing his wish that there were more than just men (also ladies!) rather than 「だらけ」 which expresses a strong negative evaluation of the fact that there are too many men.
To sum up, 「だらけ」= too many 「ばかり」= only 「ばっかり」= only (and I wish there were something else)