For both types of visas, you have to go through the same route to get a green card. Usually, you do PERM, I-140 and I-485. The advantage of an L-1B is that there is no numerical cap, so your employer can apply for an L-1B for you now. For a cap-subject H-1B, your employer must wait until April1, 2012 to petition for you, and you must wait until October 1, 2012 to start working. However, the L-1B is limited to 5 years in duration with no extensions after that. The H-1B is limited to 6 years,...
Despite the fact that you overstayed, Canadian citizens not issued I-94s who stay longer than permitted are considered "status violators" and are generally not subject to the 3 and 10 year bars. Therefore, based on what you have stated, you do not need to submit an I-601 waiver.
Carl Shusterman, Esq.
Former INS Trial Attorney (1976-82)
Board Certified Immigration Attorney (1986 - Present)
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