It's a question if one of the countries finds out you are applying for the PR of the other at the same time that they don't take your application seriously. I still don't think they would find out necessarily. I don't think US immigration and CIC talk to each other that much.
You can not maintain both PR's though if you get them both or it would be very hard. For the US green card, you can not be gone from the US more than a year at a time, preferably 6 months if you don't want to get too many questions on re-entry. Some years ago, I knew people who maintained a US green card for years by coming to the US every 6 months. After 9-11, I think they watch it a lot more closely who is actually staying and who is not. The border guards can take your green card at any point if they don't believe that you are living in the US anymore, even if you were gone less than 6 months. For the Canadian PR, you need to be in Canada at least 2 years out of every 5. Theoretically you could stay 6 months in each country, maybe 7 in the US and 5 in Canada every year to cover both PR's but it would be hard to find jobs that would allow you to do that.