What are the benefits of a six-month multiple entry tourist visa over a standard 60-day visa extension in Thailand?

No visa grants you entry in to Thailand. That is up to the immigration officer that gives you permission to enter. What it grants you is the right to stay for x number of days if allowed in to the country.

Where a visa may help is that the IO recognises the fact that you have a valid visa to enter and would probably be more likely to grant you permission to enter based on that.

No visa (or exempt) entry is a given. It’s up to them. If they feel you are doing something to abuse the system then they can deny you entry. Very very rarely would happen for an actual visa but it has and could.

The multiple entry tourist visa grants 60 stays during the 6 month validity period of the visa, meaning you can come and go multiple times and be granted a new 60 day stay each time you enter. Each entry can also be extended at immigration to get an extra 30 days. So if you enter on the last day the visa is valid till, you will still get stamped in for 60 days, which if extended to get the additional 30 days, means you can get 9 months out of that visa.

Lots of people are having difficulty getting back to back visa exempt tourist entry. You will not and can get nearly 9 months in Thailand if you work it out correctly

Since visa exempt went to 60 days, there is not a benefit for most people. It can help you get in if you've spent a lot of time already in Thailand and the immigration officers tell you that you need a visa and are abusing visa exempt.

Also if they change visa exempt back to 30 days which is currently a proposal with the government, then you'll receive 60 days on entry instead of 30.