If you are applying for I-129, you only need to list your Canadian passport information. If you are in a hurry, then TN is much faster/easier/cheaper to obtain. It only costs <100$ and can be renewed every-year with no limiation on the # of times. Of course you cannot apply for a GC under TN. But, once you get TN, you can still apply for H1B.

加拿大公民不需要H1就可以在美国工作的，他们是到入境处直接弄个什么TN证呀？记不得了，反正就是不需要H1的，我朋友的JJ就是这样的，到美国来找工作，然后找到了，马上到边境去办个什么卡就可以工作了。

我们这里有中国人拿到加拿大passport申请H1的，为了可以申请美国绿卡。