My first question would be if both are written in the same language why do you need two sites?
Yes you may encounter duplicate content issues, causing one site to rank and the other not, and you are splitting your link popularity between two sites ( why have 2 sites each with 10 links pointing to them when you could have one site with 20 links pointing to it) but more importantly you are likely to confuse your visitors.
Is there any thing stopping you using a 301 redirect to redirect one url to the other, that way you can use both URL's but only have to worry about one site.
I don't want to hijack the thread, but in my case. we've got lots of information about our products and then an online shop. The information is 90% of the site. I'd make sure the .co.uk is UK English and .com US English, however there aren't that many differences between the two.
Personally when reading a site I generally feel more comfortable when it's in my language (UK English), and when it's got US English everywhere I kinda get the feeling the company is not in touch with what I need.