Other than HBS, the interview isn't a central part of the application. It's just another data point for most applicants.
My suggestion is that if it's convenient for you, by all means schedule an on-campus not because there's some categorical bias from the adcom standpoint, but moreso because you may feel more energized and enthusiastic being in that school environment - in other words, go if it would be to your benefit rather than for the benefit of the adcom.
Keep in mind that plenty of folks have gotten into b-school having interviewed with adcoms and plenty who have been dinged by doing on-campus interviews.
As for differences, it comes down to style. Adcoms tend to be 'by the book' - it will feel more like a traditional question-and-answer interview - very structured and usually doesn't last long at all (they usually keep it to 30 minutes at most schools). The tone is usually cordial.
Alums on the other hand tend be harder to predict. The overwhelming majority are definitely more informal, and it will feel more like a conversation. Rather than taking place in an adcom office, it will usually take place in their own workspaces, at a coffee shop, in their home (sometimes), and such. It's less Q&A and more chatty.
So it's really up to you what you're more comfortable with, and more importantly, what is most convenient for you.
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