I have used both red wine and port in meat sauces, and my decision is usually based on two things:
1. What's left over?
2. What meat am I cooking with, or what is the sauce going on.
As has been mentioned, port is much sweeter, but it also should be noted that it has a much higher alcohol content, so it will help release that much more flavor from the meat and other ingredients. However, this extra flavor could be masked by the flavor of the port itself.
My rule of thumb is that pork and duck will benefit from port, whereas beef absolutely does not. Chicken and turkey could go either way as they are relatively neutral flavors to begin with.
And as was said before, port will not match well with tomato, and that is true regardless of which meats you are using.