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I'm just trying to work around the whole "Adverbs are the devil" rule. Is there any difference between these two lines in regards to writing quality:

He smiled patronisingly at them

And

He had a patronising smile on his face

Is the second option better than the first one?

Well to start with, "Adverbs are the devil" is not a rule. It is not even correct. Adverbs are a perfectly peaceable law abiding part of speech like any other.

That many people use adverbs poorly is a valid observation (thought not a rule). A reasonable rule would be, if you want to write well, learn to use adverbs appropriately.

As to your two examples, there really isn't much of a difference between them. But notice how the emphasis changes between them.

He smiled patronisingly at them

This describes an action: smiling. It is a verb. There is motion in it.

He had a patronising smile on his face

This describes a thing: a smile. It is a noun. It is static.

This difference between static and active matters a lot. There are time when you want static and times when you want active, but as a general rule, where you have the choice, the active is to be preferred unless the static produces a particular effect that you want.

And this is something that we can say in favor of the much maligned adverb. Verbs are often considered more powerful than nouns (though we can certainly take that idea too far). But verbs may need to be modified from time to time in order to describe an action precisely, and that is the job of an adverb. If trying to avoid an adverb leads to replacing a verb/adverb combination with a noun/adjective combination, chances are it has made your writing weaker.

The reason for the "adverbs are the devil" rule is they are generally "telling", not "showing".

The reason we want to "show" instead of "tell" is that it is the writer's job to assist the imagination of the reader.

To do that, we need to appeal to their senses, primarily visual and auditory, but also senses of heat, humidity, touch, and emotional feelings of the POV characters.

In your case, a "patronizing" attitude would be better expressed by letting the reader realize it is patronizing by whatever the character said, instead of just telling us it is a "patronizing" smile. What is that actually like?

It is like an adult talking to child, it is smug, and that is something you can show us.

Yes, adverbs are a part of speech, but so are tones of voice, so are facial expressions, so is volume and the way we draw out words or clip them or say them with force. The job is to stimulate the imagination with a complete scene.

Using an adverb informs the reader of a fact, but leaves them on their own for imagining how that played out.

The adage of "show don't tell" originates in theater and film, where it can be taken more literally. A character behaves as if they are angry, they don't say "I am angry."

In print, people that argue "it is all telling" are missing the point; in print the distinction is the same as in film: Does the audience imagine a character behaving as if they are angry, or does the author just tell us, "Cindy is angry" ?

Writing that helps the reader imagine a scene and action is better than writing that doesn't. Adverbs are very weak tea in the imagination department, and a shortcut that should seldom be taken, but replacing them with another form of "telling" doesn't help the situation. This is what you have done with your two examples.

Is there any difference in this between him looking smug, or condescending, or as if he is superior? I don't think so. The acts of being patronizing would be more specific and concrete, as would the experience of being patronized, either would be better aid to the imagination than just telling us his smile is patronizing.