And now let's look at the past 3 presidents: always the same routine, the EP gets presented with 1 candidate and can say yes... or yes. Awesome democracy.
Living in a small, entirely democratic EU country, I can't say I'm impressed with how the Commission was formed and it's also obviously an inferior system to that of the USA.
The power to directly elect or remove the top spot is certainly an important facet of democracy, maybe even the most important, but it's still just one of many measures. to be honest I don't think it's really that meaningful to talk about one system being "more democratic" than another, or that "entirely democratic" can apply coherently to anything except some kind of anarchist utopia.
That said, there is such a thing as the global [democracy index](https://en.wikipedia.org/wiki/Democracy_Index) in which the US comes well below the UK and plenty of other EU countries. Note that Norway, also a constitutional and hereditary monarchy, tops the list.
This is rather meaningless as an indicator of the quality of the political system. The USA was downgraded there in 2016 for various reasons (probably mostly "Trump anxiety") while the political system was left unchanged.
More concerning is the inability of the European Parliament to repeal legislation, but things are gradually moving to change this.