The issue with applying for a green card while on a TN is simple. The TN is non-immigrant intent while the H1-B can be dual-intent. There is absolutely nothing wrong with applying for a green card while on a TN. However, if for any reason, you are denied, you have now shown immigrant intent making it impossible to continue on a TN. You can, however, continue on an H1-B because it allows for dual intent.