This is pretty much just my opinion (although I do have some experience and facts for support), but I think API test kits get a bad rap here because they are inexpensive (so perceived as 'cheap') and they are easy to use (if it isn't hard to use, how good could it be?).
I used API when I started 15 years ago and then switched to Red Sea and then Salifert. I now use API on a regular basis (every 3 or 4 weeks) and if I get a wacky reading I'll double check it with the API and then with a Salifert. I almost never see much variation between the API result and the Salifert result.
My experience has been like thegrun said above, that they are all somewhat inaccurate and API is just as reliable as any, but it doesn't claim the accuracy the others do. That is, API says alk is 7 or 8 or 9 and the others will say your alk is 7.3 or 8.1 or 9.7. It looks more accurate, but is it really? And accuracy is really less important than reliability and consistency which means stability in the tank.
Our club did a big group test with lots of different test kits and different people using them. They all used the same water and the results were all over the map. So the person doing the test is just as likely, maybe even more likely, to be the reason for a bad test result