There are several important differences between an H1 visa and a green card.
Length of Stay
Unconditional (10-year) green cards are permanent. Green card holders are not limited to the amount of time they are allowed to remain legally in the United States. H1 visas are temporary, nonimmigrant visas that are issued, in most instances, for a maximum of six years in two three-year allotments.
A green card allows the holder to work in any job and in any industry anywhere in the United States or its territories. H1 visas are working visas and are limited specifically to the sponsoring employer; the visa holder cannot change jobs or move elsewhere without also changing his visa.
Green card holders can come and go from the United States at will as long as their card has not expired and they have a valid passport. H1 visa holders must have a valid H1 visa stamp placed in their passport from a U.S. consulate abroad (this does not apply to Canadians), and are limited in traveling to the dates specifically identified on the visa stamp. Also, some H1 visa holders are only be allowed a certain number of trips in and out of the U.S. during the period the H1 is valid.
Green card holders can apply for U.S. citizenship after five years of status as a green card holder (three years if married to a U.S. citizen), assuming they have no serious criminal convictions. H1 visas do not allow for such a transition. An H1 holder must first obtain his green card, then apply for citizenship, if desired, after the requisite time period.
Depending on the severity of the crime, and the frequency thereof, green card holders are generally afforded more leniency if they commit a crime in the U.S. H1 visa holders are under very strict scrutiny, and can have their visa revoked and be deported for any simple or lesser criminal matter such as a DUI.
Rights and Privileges
Green card holders are generally afforded the same rights and privileges as U.S. citizens except for the right to vote. H1 visa holders are truly considered "guests" of the country and cannot partake in many of the rights and privileges given to green card holders such as the right to serve in the military.