Should I use a K-1 visa and marry in the United States or marry in Thailand and use a K-3 visa?

Each situation is unique, so we can only generalize.

Fiancee Visa (K-1)

Advantages

1. You don't need to marry immediately, either in your Thailand or the U.S.
2. You can take your Fiancee to the U.S. and have 90 days to marry. This allows you both to get to know each other better and make a better decision about whether you want to spend the rest of your lives together.
3. You deal almost exclusively with the U.S. Immigration system and U.S. immigration officials in the United States.
4. Your fiancée has a chance to see the country and get familiar with U.S. customs and language before the marriage.

Disadvantages

1. Your Fiancée must make a strong effort to convince the Immigration Officer at the U.S. Embassy or Thailand that you are both in love and are planning to get married upon her arrival in the U.S.
2. Close family and friends will NOT see your Fiancée get married in the U.S. unless they could manage to obtain another type of visa such as a tourist visa, which is hard to obtain.
3. After marriage you'll have to file for the Adjustment of Status Application and wait for months during which time your wife cannot travel freely without obtaining travel parole every time she travels outside of the U.S.

Spousal Visa (K-3)

Advantages

1. You are both together immediately. Your wife's family and friends are able to attend your wedding without any delay, which is very important for your Thai bride
2. All you need is your passport and the "Affidavit to Marry" acknowledged by the US Embassy
3. Local marriage in Thailand can be arranged in one day
4. With a Spousal visa your wife gains U.S. legal residency immediately. So future immigration work is substantially reduced. There is no need to file for the Adjustment of Status Application and wait for months during which time your wife cannot travel freely without obtaining a travel parole every time she travels outside of the U.S.

Disadvantages

1. If you wish to have your wife in the U.S. sooner you'll have to file the K-3 Visa after you have filed the I-130 (Spousal Visa)
2. The expenses will be about 50% more

To find out more, contact U.S. Embassy/Consulate http://travel.state.gov/visa/questions_embassy.html