I've been avoiding this topic, because as stated above, the only way for the OP to solve this question is to do his own side-by-side comparison between his strips and the API Master Freshwater kit. Not all strips are created equal, I'm sure that some brands may be more accurate than others, and it is very possible that the strips have all gotten a bad rep because some of the more common brands aren't the best.
A quick search on Google will bring up several posts on other forums where people have done side-by-side testing using both strips and liquid, and share their results. Most of the ones I saw came to the conclusion that the liquid was more accurate, but there were a couple who didn't see any problems with their strips.
All of this information is only as accurate as the person doing the testing, so regardless of their conclusion, I would not personally trust their results. There are many factors that can effect the results you get from your tests, and since I was not there to witness how their vials had been cleaned, how long the strips were out of the water, how long they shook the nitrate test, etc. I would take their findings with a proverbial grain of salt.
I have used one brand of strips - Tetra EasyStrips, I had a 5 in 1 strip with 3 color pads that tested Ph, Kh, Gh, nitrates, nitrites, and a separate strip for ammonia. I have only used one brand of liquid - API's Master kit, and based on my personal experiences with both of these methods, I decided to stick with the liquid testing kit, as the results seemed to be the most accurate and consistent - as well as having a lower per test price-tag.
I was very new to the hobby when I was using the test strips, and the tank was cycling with fish-in. I was testing very frequently, in the hopes of keeping my fish safe through this process, and learning about the nitrogen cycle at the same time. I was very confused when I was using the strips, because all of my reading was telling me what to expect from a cycling tank (ammonia spike, nitrite spike, nitrate spike, etc) but my strips weren't confirming that consistently at all. Because of the inconsistency in the numbers I was getting, and after seeing API's Master kit so highly recommended, I purchased the liquid set to confirm that I was getting accurate results. I wasn't.
I often (but not always) got very different readings from the two kits on ammonia, nitrites, and nitrates - though sometimes
they would be fairly close to each-other or the same. I kept a log of my test results, and I never was able to find any consistency or pattern to the readings I was getting from the strips, where with the API kit I was easily able to track a rise and fall pattern as the tank went through it's various spikes (and water changes) before the cycle completed, and things settled down.
I also found that the strips were very
off in Ph, Gh, and Kh. Although both types of test came up consistently with the same numbers every time, they were very different from each-other. The test strips showed my water to be fairly hard, ideal for the live-bearers who were living there at that time. But the API liquid test results show my water to be soft with a neutral Ph. A call to my water supply company confirmed that the results I was getting from API's liquid kit were correct, so I trust those results (as do my soft-water fish!)
A bit more information. . . I was very careful to keep the test strips dry and away from humidity. I kept them in my cool but not damp basement, the bottle of strips was tightly closed after use, and kept in a sealed plastic container. I even went so far as to put a packet or two of silica gel into the box (not the bottle) because I read that they were very susceptible to inaccuracy because of dampness and humidity, etc. The bottle only lasted about a month, had been purchased brand-new and sealed, and I'm fairly certain I did everything in my power to make sure those strips were not contaminated by moisture.
I also found very quickly that the vials that are sold with the API kits are inaccurate, and vary slightly from vial to vial. I do not do my tests based on the 5ml line marked on these vials, I measure out 5mls of water into each vial from an oral syringe to ensure the proper amount of liquid is being used. I have found that many things can affect the accuracy of the liquid kits, including how the vials are washed/rinsed/dried between uses, and that the regents, especially the nitrate, are properly shaken before use.
Unfortunately, I no longer have the log that I kept while using the strips. Once I came to my own conclusion that they weren't giving me accurate readings, I felt no need to keep the information I had written from them - it was only confusing things - so I discarded those pages.
A friend of mine started her tanks at the same time as I, and she had a very similar experience with another brand of test strips. . .
Again, the only way that the OP will be able to come to a proper conclusion is to test the accuracy of these types of tests for himself. It is also worth noting that the tests we use for our aquariums, though they are good for what we need them to do, are in no way showing everything that is going on in our tank. Despite what the packaging may tell you, these tests are nowhere near accurate enough for use in an actual scientific analysis. However, for our needs in keeping our fish happy and their water contaminate-free, they do the job. . . well, the liquid kit does, anyway
Hope that helped somehow. . .good luck with your own experiment!