It can vary depending on the size of the transaction data, so there is no simple answer for this.
The attack you are referring to is not likely. In that attack, malicious nodes nodes were encoding identifiers into a spot in the header of data being sent. Other malicious nodes would later be able to decode that data to identify that it was the same chunk seen earlier. When the attacker had a lot of nodes, this allowed the attacker to find out what user ip was connecting to service ip, but only when both the first and last nodes were owned by the attacker. The attacker still couldn't read any of the data being sent, they could only see that a connection occurred. Since the attack is about abusing the ability to encode some data into headers, the problem is not with the idea, but the implementation.
In the darkcoin version, the protocol will most likely be much simpler than tor, which results in less places to attempt to hide things, and should be easier to secure. Without a place to stash data, in order to identify an ip to an address, the attacker would have to own all masternodes involved(3 for obfuscation + selected masternode). Since coins are mixed several times before being used, even if the attacker was to get lucky and have a transaction go through only nodes owned by them, it wouldn't likely tell them much, as it would only be one step of mixing they see. For an attacker to be lucky enough to see a whole set of mixing cycles for some coins, they'd have to own a significant portion of all masternodes, which would be very costly.
