applying for a new job with a TN visa

I am a Canadian working in the US as a veterinarian. I have been here on a TN visa since July 2006. My visa is due for its second renewal June 2008. I am currently looking for a new job. I am not sure if I should accept a new position before my current visa expires or if I should renew it with my current job, then apply for another one with a new employer. I cross the US/Canadian 4-5 times a year. My worse fear is getting denied entry into either country.

At this point in my career, I plan on being in the United States for awhile. Would it be more beneficial to apply for a green card instead of a TN visa?

I hope someone can help.
Karen

If you qualify for permanent residency, then obviously it would be better to get it. If your employer is willing to do the paperwork, etc.