You will hopefully make the choice of whether to marry a U.S. lawful permanent resident (a green card holder) or a U.S. citizen based on personal, not immigration considerations. You will be eligible for an immigrant visa and green card in both cases. Nevertheless, there is no doubt that marrying a U.S. citizen leads to a faster green card, as described below.
If you are married to a U.S. citizen, you will be eligible for an immigrant visa (if needed for U.S. entry) and then a green card (lawful permanent residence) under the Immediate Relative category. This category has no numerical limit on the number of visas issued each year, and therefore no long waits for visas/green cards to become available.
Getting through the application process is likely to take several months, starting with filing an I-130 petition. There is no getting around that, however, regardless of which category of green card you apply within.
After you are approved for permanent residence, however, the very speed with which you got through the process may introduce one inconvenience: If your marriage was less than two years old at the time you became a U.S. resident, your residence will initially be only "conditional," and you will see a two-year expiration date on your green card.
The idea is to give the immigration authorities a second chance to judge whether your marriage is bona fide, or the real thing, not just a sham to get a green card. For more information on this part of the process, see How to Manage Your Conditional Resident Status.
There's yet another benefit to being married to a U.S. citizen: Three years from the date you become a permanent resident, you can apply for U.S. citizenship, so long as you remain married to and living with the citizen. Most green card holders have to wait five years before applying for U.S. citizenship.
If you marry a U.S. permanent resident, you must apply for an immigrant visa under the Family Second Preference category. The number of visas/green cards issued each year under this category is limited, and the demand is always higher than the supply.
Applicants do not normally receive a visa number (which is required in order to get a green card) in the year their U.S. spouse first files the I-130 visa petition for them. Instead, they are put on a waiting list, based on their "priority date" (the date U.S. Citizenship and Immigration Services or USCIS received their spouse's I-130 petition).
The waits are typically around five years long, depending in part on which country you are from. (Per-country limits apply, and demand tends to be particularly high from India, Mexico, China, and the Philippines.)
You must wait for your priority date to become current before you can take the next step and apply for your immigrant visa and green card under this category. (Learn to track the progress of your priority date.) Then, like people who are married to U.S. citizens, you will probably have to get through some months' more worth of application processing.
One benefit of having already waited this long, however, is that once you're approved for residence, it's likely to be permanent, not conditional residence (the latter, temporary status being given to people whose marriages are less than two years old at the time of their approval).
Given this long wait, it would be beneficial for your permanent resident spouse to look into applying for U.S. citizenship as soon as he or she is eligible for it. More information on this can be found in this overview article on Steps to Become an American Citizen.
If you're looking to get a family-based green card, you may want to talk to an attorney to find out if they can help with the process. Hiring an attorney to help with the petition process adds legal fees, but a professional may help to expedite your case and avoid any legal problems.