I happened to find something while cleaning my house and with E3 coming up next week seems like a good time to share this.
When I was on on God of War - one of our main competitors was Capcom's Devil May Cry. After God of War 2 shipped, our creative director Cory Barlog, sent basically a care package to their team. It included a copy of the game and a letter saying how awesome the whole team thought their games were and how strong of a team they were. I unfortunately don't have a copy of the letter that was sent but I do have the response from the Devil May Cry team.
Note that clicking on the link sends you to a PDF of the image above.
I think as game developers we really need to communicate and share with one another more often. It makes all of us better at our jobs.