which is the most accurate, the d fantatix analog or digital battery checker?

I purchased both the digital (Model BT 168D), and the analog (Model BT 168). Cheap enough and wanted to have them available in multiple locations without hunting it down each time such as basement, garage, other home. They both seemed to work until my electrical product failed. The analog showed battery still good, solid green reading. The digital read 1.3 volts for a 1.5 volt battery. I then checked against my higher quality voltmeter, which also measured 1.3 volts. Usually the analog has a red-yellow-green zone, but in this case the reading was definitely in the green zone, not even borderline. Since this happened I’ve tested on a few more batteries, and decided to throw the analog device out. Unless the battery is DEAD, the reading is misleading. In the digital era no point in wondering.

I keep seeing people ask about "load" checking. Is that important? I just want to know if my batteries are still good

A moderate load is important to check AAA, AA, C, D and 9v or any other battery for that matter. The reason is the open circuit voltage check does not indicate if the battery has the Current capability to sustain the nominal 1.5 or 9.0v under a light to moderate load for a brief 1-3 seconds. Even with a loaded test, it does not indicate the remaining Amp Hours. But a loaded test is a quick and easy light weight check and is a step better than not loaded.

Does it test button batteries, like CR2025?

I'm pretty certain, after multiple testings and wasted batteries, that it does not work for 3V buttons - and it can actually damage them. I've tested multiple 2032 (and bigger ones), old, new (bought years ago), new bought this week. Most will show green for a short while, then it will drop, all the way into red. It takes different time to drop to the red zone. And I'm pretty sure the "drop" is actually the process of draining that battery because then the "new" battery wouldn't even work (in my car remote). I will upload the video if I can figure out how.

Will this test a cr123a and/or cr2 batteries? thank you

CR123A and CR2 are 3-volt, tubular batteries. The meter's full scale is little more than 1.5 volts. The voltages are too high for this type of meter. Do not test these batteries.