I don't think the real conjoin is the optimal choice if you are aimed solely to consolidate UTXOs. For privacy improvement, it is likely Yes, but for single consolidation purpose it would be overkill. Besides the more relevant techniques are in your arsenal the better. BTW, if you lean towards real conjoin , Sparrow offers this option via mixing with wirlpool.
Fake coinjoins use the same amount of block space as regular coinjoins, there's no reason to limit the number of participants in your consolidation transactions to yourself. Unfortunately, Sparrow's Whirlpool implementation does not offer private input consolidation like the WabiSabi coinjoin protocol does, so you reveal common input ownership when entering the pool:
https://bitcointalksearch.org/topic/--5286821About better or not that is suggestive no?
No, it's literal: If you are trying to privately consolidate your inputs, each marginal input added to the transaction that doesn't belong to you increases your privacy.
The point of a fake coinjoin is that it looks like a real coinjoin and only the people who participate on it can spot it as a fake coinjoin, all outside just can see a real coinjoin transaction.
Or can you spot the difference between them and tell us what is a fake coinjoin and what is a real one?
It depends on your coin control. If you merge your faked outputs in the future, then it doesn't help.