There's nothing much of difference if you think from the privacy view. DeepOnion is using DeepSend to hid tx details (although it's not tested in a large sum, not tested by any chain analysis) while Monero uses RingCT to hide tx details.
You can check more here, but don't laugh at the poor guy's comment (they all were noobs back then)- https://deeponion.org/community/threads/monero-vs-deeponion.4894/?amp=1509283365