Two small additions to Dan's good answer. First, I agree that devotion implies emotion and dedication implies reasoned commitment or duty. But I don't think devotion needs to be romantic. People can be devoted to family members, a religion, or caring for a pet. Second, there's an additional meaning of "dedicated to." It can mean that you are honoring someone. Books have dedication pages saying in whose honor the book has been written. (This is different from the acknowledgements, which are thank-yous.) A library may be "dedicated to" the person for whom it's named or the future generations of students who will use it. Back in the day, you could call a radio station and ask to dedicate a song -- that means you're asking them to play the song in honor of someone you know and announce the person's name.

There may be a better classical answer, but I'm going to say what I see at first glance... Compare to = Compare with. They mean practically the same thing, practically all the time. The difference is miniscule. There's just a slight difference in tone. Using 'with' usually sounds a bit more precise & formal - sometimes this is helpful, but sometimes it's too much to the point of sounding awkwardly unsmooth - it depends on the exact sentence & context. 'Dedicate to' can mean the same as 'devote to' in many contexts. They have very similar meanings. But 'devote' is more often used in a romantic context, while 'dedicate' is more often used in a hardworking context where emotion is not involved; and this may be worth considering to avoid inappropriate intonations.