AWS becomes interesting when you want to automate your infrastructure (i.e. infrastructure as software). When you're not orchestrating your infrastructure, then its probably overkill.

DO, as you rightly mentioned, is a lot closer to a straight forward Linux or whatever instance (easier to use). And the prices are very attractive.

I use both and split based on the above. DO is great for hosting web apps / dynamic web sites at a reasonable price. AWS is great for orchestrated clusters / large scale production, or for very low cost static hosting via S3.