Aside from one being a fruit portmanteau and the other a vegetable.. they don't have much in common with regards to privacy. DeepOnion says it offers untraceable anonymous transactions but I can't seem to find any information on how they are achieving this.. from what I can tell, they are overstating their capability. DeepOnion advertises TOR support.. nothing big there.. Bitcoin has supported that since around 2012.

On the other hand, as one of the original Cryptonote projects, Boolberry was built from the ground up to offer real privacy mechanisms: sender privacy through ring signatures (1/N probability) and receiver privacy through stealth addresses.

For more information on Boolberry works along with a comparison to traditional Cryptonote check the links below:

Boolberry presentation explaining advanced anonymity - http://www.slideshare.net/boolberry/boolberry-solves-cryptonoteflaws-37055246
Boolberry presentation explaining smaller blockchain - http://www.slideshare.net/boolberry/boolberry-reduces-blockchain-bloat
CryptoNote technology description - https://cryptonote.org/inside/
CryptoNote white paper - https://cryptonote.org/whitepaper.pdf