The VPS is like renting office space. You don't own the space, but for the most part get to use it how you want, and all the responsibilities that come with that.
"Serverless" is like paying for a hot desk by the minute, with little control of your surroundings, but it is convenient and cheap if you only need it for an hour.
At one job I had access to some paid AWS support tier. It's basically a bunch of consultants. We needed to process a datastream of events from user actions on a website. We asked about serverless / AWS Lambda. Their answer was something like "Well yeah it'll work but don't do that. It'll cost too much money and you'll wind up rebuilding it around EC2 anyways"
Yup. If you want something to plumb some pretty low volume events, sure serverless like Lambda can be useful. Anything which would be considered high levels of compute, you are just wayyy over paying. Hell, even EC2 on spot instance is expensive compute. I do like some AWS services, but yeah they come at a premium that is just getting more and more expensive.