I don't particularly like any of the apps I have tried, not sure about fitlist, but that includes gymaholic and Strong and Gym Log+. So none of them display my history of lifting either day by day or in terms of my personal bests, in a useful way on my phone. I can't see or find my PBs for lifts (so the day and weight) on my phone in either gymaholic or Gym Log (I think they may be buried in their somewhere though).
However, and I can't remember if I bought Gymaholic or how much that was, I do use that on my watch and for a watch app for actual use while working out, that works pretty well. So I like how it runs the timers between lifts and sets. It is really easy to set up standard workouts, which I repeat on days. It is just a button push to record each set. It is not hard to skip something in a workout when I want to skip doing that lift. I am not sure any watch app will be great if you change your weights and your routine everytime you lift, since editing that stuff on the watch in any app is not great. But in Gymaholic changing the weight or the reps is doable and does work pretty well, using the watch dial. I would just go crazy or not care enough to do that for every lift on every set. Meaning, I usually bench and deadlift and do other lifts with the same weight and the same reps, each time, most of the time. If I intend to bump up a weight moving forward, I would edit the standard workout in the setup.
There is another app out there that is supposed to automatically recognize and record your workout, including counting reps. I remembering demoing that a year or two ago, but could never get it to work properly. I mainly wanted that to count kettleball swings, which seem like a very distinctive and unique motion; but it could never track or identify or count those correctly. So the name has changed, but I think that is Gymatic Workout Tracker. that costs money on a subscription basis so not something I am going to pay for.