He paced about/around the room.
Can those words be used interchangeably? If that's the case, which one is more common?
In American English, yes, one can both pace about and around a room. Both are correct, and both mean the same thing - to walk randomly in the room or possibly along the periphery.
Around doesn't always mean on the outside circumference of something. Two relevant definitions from the OED:
About (adv): 5. In U.S.: = about adv. a. Here and there with no fixed direction; all about, at random; as in ‘to travel around,’ ‘to fool around’.
About (prep): 4. U.S. (a) Hither and thither over, at random through, about; as in ‘to travel around the country’. (b) Of time, amount, etc.: about, sometime near.
In most cases, however, about is not interchangeable with around.
Often, the preposition around is used as shorthand for around various physical spaces inside the confines of; while this is not technically correct English, the practice has certainly become accepted via folk etymology, that is, through evolution of language as it is used by laypeople over time.
One cannot, technically, pace around the room while being inside of the room; the very abstraction implied by around involves space specifically adjacent to but strictly not including (the object of the prepositional phrase). One who paces around the room technically walks near the room but not inside of it.
In contrast, the preposition about implies much more flexible criteria describing the relationship of the verb-implied-action to the object of the prepositional phrase. A common word preceding about is the verb to talk, for example, and someone who talks about the room is most likely talking such that the content of their words, or their message, is directly related to the room and its properties as a noun-thing.
It should be pointed out, however, that to talk about the room may also be inferred such as to conjure the image of someone talking, on an unspecified subject, while physically occupying various spaces inside the room.
Prepositions are probably more prone to the confusions associated with folk-etymological development than would be prone any other part of speech. This might be, in part, because prepositions are essentially pseudo-mathematical in nature, in the sense that they are used to compare, contrast, and ultimately triangulate between two or more ideas; that is, they are used to define one thing by means of/relativity to another thing.
Such insertion of very logical operation into language is recipe for confusion.
Observing this basic pattern, and following it successfully to its logical conclusion, that almost all stated ideas involving preposition-phrases can be described in at least two different manners, I find it silly to suggest that any particular preposition is correct.
And unless you can tell me right now whether I just spoke around prepositions or spoke about prepositions and back up your answer with a definitive unarguable proof, it would seem you might be wise to consider adopting a similar attitude towards prepositions in the English language.