The downside is that the PHP service environment does't provide much of a runtime framework, so the PHP application itself needs to perform a huge amount of bootstrapping on every request (this builds up over time as you add stuff to the application). Comparing this to AWS Lambda with e.g. Node.js, Lambda can keep a lot of stuff pre-initialized in memory, and usually just directly execute a handler function. Also things like URL request mapping are externalized to a separate API Gateway. There used to be a lot of tweaking and running separate caching modules needed to make PHP bootstrap fast enough.
I've always been sad that AWS hasn't developed a fully supported PHP backend for Lambda. Combined with a lightweight HTTP gateway, it could be a nice way to keep running legacy apps like WordPress in modern serverless environments, without worrying about server costs and maintenance. You can do it yourself with Lambda layers, but there will be all kinds of small mystery timeouts and problems you have to deal with.