This could be someone who probably develops PHP apps using Laravel and has probably never even used ProcessWire. I'd expect something similar from a developer whose tool of choice is WP ?. So, unless they show you some benchmarks, I wouldn't necessarily believe it. Having said that, I don't know if ProcessWire is faster than Laravel or not. About stability, ProcessWire is very stable and reliable, although I am not sure what definition of stable we are using here.
This really depends on your needs. I don't understand what you mean by 'wanting to setup a directory'. Both ProcessWire and Laravel have their strengths depending on the type of application or website you want to build. Laravel is a fine piece of kit just like ProcessWire is, however, the entry levels differ as well as their out-of-the-box experiences. The fact that you went to Fiverr tells me that you want somebody else to build the 'directory' for you? In that case, ask yourself questions such as long term support: which system (community) will serve you better in this case? E.g., if your developer 'vanished', will you still be able to use the system, get the support needed? What about scalability? Are we talking hundreds, thousands, millions of records/pages? There are many other questions but rather than throw the kitchen sink at this, maybe tell us a bit more about your 'directory' ?.
Just my 2p.