I haven't run across any trial results. I've read different things, like the new formula is not as effective, but nothing definitive. Safety seems good for all of them, especially when compared to just getting infected.

If you had a bad experience with the mrna ones you will want to seek out Novavax, which is harder to find but has less side effects and seems to offer slightly longer protection. Even though it targets a slightly older strain is offers just as much or more protection.

I cant find the sorces where I read all this at the moment, but i found this:

What’s new about this year’s updated COVID vaccines?

As in previous years, there are mRNA vaccines—one from Moderna, one from Pfizer—and a protein-based vaccine, from Novavax. One nuance this year is that the mRNA and protein-based vaccines target different—though closely related—variants.

The updated mRNA COVID vaccines from Moderna and Pfizer are based on the KP.2 strain, one of the FLiRT variants that have been spreading since early spring. These variants and their sub-variants have caused the majority of infections during this summer’s COVID wave. The protein-based Novavax vaccine is based on the JN.1 variant, which accounted for the majority of COVID infections in the first few months of 2024 and is the parent strain from which KP.2 and other currently circulating variants branch from.

At the end of the day, laboratory experiments show that all of the updated vaccines available this season can recognize circulating COVID variants and therefore should be similarly effective in reducing your chance of becoming severely ill from COVID infection or needing to be hospitalized.

https://publichealth.jhu.edu/2024/what-to-know-about-updated-covid-vaccines-for-2024-25