From a purely legal perspective not in any significant ways. However from a public opinion perspective the difference is more significant. Same sex marriage has ~90% approval rating in the Netherlands compare ~55% in US. I cannot imagine that those sorts of differences don't greatly affect the day-to-day reality living as a same sex couple.

On most day-to-day reality issues (for same sex couples or anyone else) local norms are probably much more important and I can assure you there are lots of parts the United States that have 90% approval rates for same sex marriage.

So if we are discounting the legal perspective (which just as a personal opinion, I wish the US federal law was more progressive), cherry-picking public opinion to match the more progressive parts of the sample seems like the US comes out about the same.

As for how NL is 'better' than the US: It's a ridiculously small country and very densely populated so what works here would likely not work as well in places like Canada or the US, but as mentioned above I think coalition politics (het poldermodel) is an important part of making sure that minorities do not easily become the football of dominating majorities. Both large US parties would be considered right-wing here (roughly VVD), the US has no functional left which is a residue of the McCarthy years and the cold war. Somehow the US associates 'left' in politics with 'communism' and that has kept a very large chunk of the US population without representation.

In NL it is very hard to find any substantial chunk of the population without representation. We also don't jail 1% of our populace.

That said there is plenty of room for improvement, we still have corruption, racism, crime and so on at levels higher than what I'm comfortable with, and our government is excellent at wasting money, an area they are slowly improving on but in my opinion too slowly.