I started my path down VPS hosting on DO and later Vultr - mainly for hosting clients' WordPress webservers. I think their biggest advantages are predictable pricing and user-friendly admin interfaces. It's really nice to be able to say "Hosting is going to be $12/month" and know that will be true for the foreseeable future, versus trying to explain/predict AWS' pricing which is more like paying a utility bill. It's also really easy to get a development server up and running quickly without having to worry about all the details.
With all of that said, I haven't gone back to DO or Vultr since I learned how to work AWS EC2 instances. For one thing, it's a much easier sell to say "I'm hosting your site on the same physical infrastructure that powers Netflix" than trying to explain the advantages of VPS hosting to non-techie people. With reserved instance pricing, you can really cut down on the extra costs typically associated with using AWS as well...
The biggest thing for me is that, last I checked, DO and Vultr both charge you full price for any VPS associated with your account, whether or not it's running. You need to totally destroy a VPS to stopped being billed for it. AWS (and I would assume other "big players" in this space) only charges you for data storage of stopped instances, which is a relatively tiny part of the usual hosting cost.
This is a big advantage for me as I can keep staging/development copies of webservers ready to go without paying full price for their existence or having to wait for a whole new instance to spin up. This has been really nice with the regularity of platform updates on WordPress and the importance of applying them quickly...