Often those eligible for TN status are also eligible for H-1B status and vice versa. Each route has unique positives and negatives.
The TN process is limited to Mexican and Canadian citizens. It is cheaper, quicker, and happens on a much more flexible schedule than the H-1B visa process. TN visas are issued for period of three years, and may be extended an indefinite number of times. However, it is limited to the professions listed in NAFTA, and an applicant must have the qualifications specified for each profession in the treaty. Usually this means a bachelors or advanced degree, and there is no flexibility to substitute work experience for the degree requirement. The TN visa process also requires that the applicant prove “nonimmigrant intent,” meaning an indication that the applicant hopes to immigrate permanently to the United States could be ground for denying TN status.
H-1B status, on the other hand, is open to citizens of all countries. It allows for “dual intent,” meaning a person may remain in H-1B status while also pursuing permanent residence (green card) in the U.S. H-1B status is also available for a wider variety of professions, and a person may qualify for an H-1B based on either a degree or equivalent work experience. The application process, however, is more expensive and complicated, takes longer, and requires heavier employer involvement and expense. It lasts for a maximum of six years.*
The decision about which route is right for you will require a thorough analysis of your situation and future plans.
* Unless the H-1B holder has a pending employment-based petition for lawful permanent residence (green card), in which case the H-1B status may be extended indefinitely if certain conditions are met.