[Denis DNT]

This has been a headache for the past two weeks. What's the right one?

[mesmark]

both are fine, in my opinion. Do you have an example sentence?

[Denis DNT]

1. Teaching adults is more enriching compared to / with teaching kids.
2. I am trying to compare the movie The Day After Tomorrow with / to 2012

[susan53]

Yes, both. I checked with a concordancer and there is no difference even if you compare eg British/American usage, or written/spoken. Nor does the following phrase have any influence (eg is it followed by a gerund, a noun phrase, a number or anything else). It always comes out about 50/50. Individual speakers might have personal tendencies to use one rather than another, but there doesn't seem to be any specific rationale behind the choice

[mesmark]

I was running some examples through my head (a completely trustworthy and scientific method :P) and what I find is that I tend to use "compare to" when I'm showing contrast and "compare with" when I want to express similarities.

"This is nothing compared to the storm of '97."

"Compared with the storm of '97, we see that high pressure systems preceded both disasters."

So in your examples I would probably use "to" in both examples:
1. Teaching adults is more enriching compared to teaching kids.
- the sentence implies they are very different - contrast

2. I am trying to compare the movie The Day After Tomorrow to 2012.
-this example is a little less clear for me. I need the context of surrounding sentences but I'd most likely use "to"

Anyway, I still stick with they are rather interchangeable. Those are just some thought I had on the matter.

[Denis DNT]

Thanks Susan and Mesmark. It had never crossed my mind to think about the two until recently a student asked me in class. My colleague insisted "to" was more in use than "with".