Any equivalent to this Persian proverb "The yellow dog is the jackal's brother"?
I would say:
Meet the new boss, same as the old boss.
This means that although the parties in charge have changed, the living and working conditions have not.
It apparently comes from they lyrics of The Who's song Won't Get Fooled Again by Pete Townshend.
There's small choice in rotten apples.
A choice between the Devil and the deep blue sea.
It's six of one and half a dozen of the other. (One person is as bad as the other).
This is a similar situation that recently happened at my work place, except that I found out firsthand how much worse my new boss is compared to my old boss. Referring to the impact this new boss has on our work environment, I warned a colleague who like me, initially had positive expectations of the new boss, by telling him, "We're out of the frying pan now!"
The idiom "out of the frying pan and into the fire" described for me the exact situation in which I had found myself: I thought that my troubles at work would depart with the old boss, and that things would greatly improve, but instead with the new boss only came new treacheries.
While "wolf in sheep's clothing" would apply to the face of innocence this new boss uses as a mask to cover inner-evil, it doesn't fully describe how much worse the new boss is in comparison to the just-as-awful-in-a-different-way old boss. "Lesser of two evils" also has similar meaning - that with one or the other the fact of accepting evil either way still remains.
Your use of "each of them is worse than the other" is a perfect description! It is helpful to have a phrase that describes these boss-entities separate from my own frying-pan experience, but I don't know/can't find an idiom that I feel really fits yours.
The difficulty is in matching the meaning and the use of predatory animals to describe the characters of people in relation to each other and to the proverbial village upon which they prey. It is the implied inherent tendency to predation in "the yellow dog is the jackal's brother" that is hard to match. To describe both bosses as one predacious entity you could say "you can't take the jungle out of the tiger".
(For lack of a traditional idiom or proverb, or even just an English colloquialism that can represent the archetype, I just refer to my new boss as "President Coin" after a character in the young adult dystopian fantasy series "The Hunger Games".)
Consider,
A new broom always sweeps clean [at the beginning]. Wait until a few bristles have worn (=until the novelty/shine has worn off) and you'll see it doesn't sweep any cleaner than the old one!
Damned with one, damned with the other.
two sides of the same coin
If two things are two sides of the same coin, they are very closely related although they seem different (emphasis is mine.)
Cambridge Idioms Dictionary
Editorial: Donald Trump and Ted Cruz are two sides of the same coin
Ted Cruz is not an acceptable alternative to Donald Trump. They are both dangerous demagogues.
Cap Times
cut from the same cloth; made from/cast in the same mold
Meaning: Be very similar, act in a very similar way
If you say two or more people are cut from the same cloth, you mean they are very alike or act in a very similar way.
OELS
speak the same language
To share similar beliefs and opinions.
Cambridge Dictionary of American Idioms
Sounds like they were both tarred with the same brush.
tarred with the same brush
Having the same faults or bad qualities, as in He may be lazy, but if you ask me his friends are all tarred with the same brush. This term is thought to come from sheep farming, where the animals' sores were treated by brushing tar over them, and all the sheep in a flock were treated in the same way. The term was transferred to likeness in human beings in the early 1800s.
tarred with the same brush. (n.d.) McGraw-Hill Dictionary of American Idioms and Phrasal Verbs. (2002). Retrieved April 20 2016 from http://idioms.thefreedictionary.com/tarred+with+the+same+brush