Guide to A-Z+T for the Ordinary Working Linguist
Perhaps the first and most important thing to realize is that A-Z+T is not designed to replace FLEx. It has a different orientation, different intended audiences and different functions, and this is by design. So if FLEx does everything you want to do, then you will probably be happier just sticking with it.
Most of the same could be said of WeSay, though the audiences would be more similar.
Perhaps the second most important thing to say is that A-Z+T is designed to facilitate a participatory model of data collection, not just give you another way to collect data as you may have been taught in a field methods class.
So if you're sitting down in a field context with someone who doesn't have a high school degree, you aren't likely going to hand him the mouse and keyboard and ask him to make changes in FLEx. FLEx just isn't designed to be used that way, but A-Z+T is.
To use A-Z+T well, you want to gather a number of people who are proficient in their language and ready to discuss it with each other, and hand one of them the mouse. The keyboard is relevant for some tasks, but that should be operated by them, too. You may guide, direct, and/or provide feedback on the conversation, but the decisions should be registered with A-Z+T by the speakers of the language, not you.
Some people like to see things in context, in order to understand them better, and to know how to fix them. Others are happier with lots of abstract options to pick from at any given moment. Neither of these are better; this is a difference reflected across cultures and personalities.
FLEx is designed for people who are more comfortable with computers, and provides options to filter and sort data in almost any way you can imagine. If you like spreadsheets, you probably like FLEx.
A-Z+T, on the other hand, is designed for people who want to do a specific set of things, perhaps in a specific order, without needing a lot of options. On most pages, the user clicks one button at a time. Or, if there is a field to fill in (like for the word list collection), there is one field presented at a time. A-Z+T specifically avoids offering a user the chance to put good data in the wrong place. So if you've ever been confused, frustrated or lost using a spreadsheet, you should enjoy using A-Z+T.
In terms of functions, both A-Z+T and FLEx (or WeSay) could be conceived of as dictionary builders. But FLEx (and typically WeSay) build data one entry at a time, once sense at a time. If there is a problem with data, you go in to that one entry/sense, and find the field with bad data, and change it.
A-Z+T, on the other hand, treats data in relevant groups. If a number of words sort together, and there is a problem with them, it is fixed once for the group, rather than in each entry/sense. Words can be sorted in and out of groups, but there is no way to change the data on an individual word, entry, or sense.
So, if you are a person who likes to check and correct data word by word, you will probably be happier with FLEx or WeSay. But if sorting words into relevant groups before correcting them makes more sense to you, you may be happier with A-Z+T.