I am more concerned about doing things correctly. I have been known to always be slow at some things but this is because I am more concerned about doing a good job on everything that I attempt to do. I think that it is important to tackle things and do them correctly.
This question is difficult because I don't believe in an objective sense of "correct." I chose doing things correctly because this allows me to apply my own standards to everything I do. Saying that it's more important to do correct things implies that I'm not doing things I deem "incorrect." I don't believe my standards for correct are any better than someone else's, so I'd rather focus on doing what I believe to be the right thing in everything I do, rather than choose the things I do based on my personal standards of correctness.
I could do a lot of bad things if I simply did things correctly. I tend to be more concerned with doing correct things. All of this is quite subjective because I am given multiple options of which I have to assess each to determine what is right for me or whoever else is involved.
Saying we are concerned about doing things in the correct way means that we are seeking perfection and that is never able to be attained. But if we seek to do the correct things, then we are talking about doing what is right and doing what is right for us in a particular situation which has some integrity.
I hope I'm understanding the question correctly, but I live my life trying to do the correct things. By correct things, I mean trying to be the best version of myself possible and trying to be the kindest I can possibly be to other people as well. Best way to live.