If you are an individual, almost certainly, unless you are using LLMs very heavily.

If you are a business employing many people all of who use LLMs reasonably heavily? You can still spread the hardware cost over many users and respond to multiple prompts in parallel. At some point buying the hardware will make sense.

I would not get a dedicated server to run a single small VPS. On the other hand if I needed a lot of capacity a dedi is cheaper than a big VPS (or lots of small ones).

There is also a benefit for anyone who has confidential or secret information.