This type scenario is becoming more and more common.
Based on my experience, I would try to sell the property 1st.
And trust me on this, a property management company can cause more headaches than just renting it out and managing the property yourself – not to mention the tenants (a property manage does not always insulate you from tenant headaches).
There are many many unscrupulous property management companies out there…do your homework.
Also, even properties in prime areas can sit vacant longer than you might think.