Legally speaking, TN can apply

green card directly. But technically it is more difficult than H-1B from substential legal requirement for specialty workers and the process time assuming. TN needs to renew every year and CIS is relactent to grant it after several years renewal. H-1B can get maximum 6 years and indifinate after your Labor cert is filed (must file on or before 365 days before your 6th H-1 expires) till you get your green card. So for your advantage, you should change your TN to H-1B first then start green card process. TN change to H-1B is not a difficult thing to do.