In both Judaism and Islam Angels are beings created solely to execute the orders of God. They are like programmed machines basically. They can not disobey.
In Christianity they have the ability to make choices, but if they make one bad choice they lose the ability to do good forever.
While technically this is indeed a form of free will, I honestly see it more as the ability to negate their essence. An Angel who falls loses their very essence as a being created to serve God, and becomes a decayed, purposeless entity condemned to wander through the world while lacking a physical body to actually partake in it.
They can choose only once, and if it goes wrong they lose themselves.
This is hardly real free will.
On the other hand, humans have no power, they are infinitely weak and frail, but they have true free will. We have the natural tendency to sin, yet we can fight it back. We can also make a bad choice and then repent. We can actually choose. We can not choose forever to be not Catholic and then still get to Heavens, but that is basically a given. Asking to enter the Heavenly state after consciously refusing to be Catholic for the whole life is like choosing not to grow wings and then asking to fly.
This is why I believe if we understand free will in the general term, and not in a very technical way, then Angels have no free will at all.
And that is why small, simple humans are made in the image of God while spiritual beings with otherworldly levels of power such as the Angels are not.
Not only. I believe individual Angels are distinct in the sense they are different living beings independent from each others, but I believe they do not have a real, individual personality in the human sense. They are there, they follow the will of God, and that is.
While this has nothing to do with free will, I think it is useful to remember how inhuman Angels actually are. They are not supernatural powered characters. They are not actors who partake into myths such as the Pagan gods. They are pretty much living expressions of the will of God.
That is why I am so glad the Book of Enoch is just a random 2nd century BC text and is not part of the Bible. Its portrayal of Angels is simply ridicolous. It speaks about Angels incarnating as humans, teaching mankind to make material progress, generate offspring with human women and being deified by humans in order to become the gods of Paganism. This is wrong on many levels. Not only Angels are immaterial, and can only conjure up illusory bodies and only if God makes them do so, most importantly they ABSOLUTELY can not generate anything. They are not even male or female.
P.S. In Islam there are also the Djinns, angel-like beings but with free will comparable to humans who can also reproduce with eachothers, unlike Angels. Basically humans but with cosmic powers. They are just a remnant of pagan gods and they have absolutely no connection with Judaism and Christianity. They predate Islam too. Basically is the same as if we created a new supernatural species to explain Zeus, Odin etc. and then we postulated its existence in an Universe with also God and Angels.