It's generally easier, faster, and cheaper, to apply for the tourist visa if you want between 30-60 days.
When you go to the airport for your flight to Thailand, the airline may require you to show proof of onward travel out of Thailand within 30 days, because that's what you will receive when you arrive. If they require this and you don't have it, they can deny boarding until you purchase a ticket to satisfy their requirement.
Also, you're going to potentially have to take an entire day out of your trip to go to the immigration office and apply for the extension, and worry about getting a TM30 from wherever you are staying as part of that extension application.
If you apply for the tourist visa online, you'll receive 60 days when you arrive. You can simply show the visa to the airline and they will be satisfied with that, and you never have to worry about visiting immigration at all during your trip. Most embassies also charge less for a tourist visa than what an extension costs inside of Thailand.
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