In days gone by, small Mackie mixers had a mic-level output, so you could plug a CD player into it, then connect the mic-out to the mic-in of a recorder. That way you could readily test recorders with an much better quality source than a live recording of a band's PA speakers, which is an inherently poor quality source. I guess a suitable attenuator would do the same.
With the samples kindly posted, I'm not hearing much if any difference, and I wouldn't expect to. As someone above says, mic quality and placement are likely to be the significant factors in the outcome (unless something is grossly wrong with the recorder), and source quality is kind of important too...
At the end of the day, there's every likelihood that the F1's internals are the same as the H1N, which is about as low-end a recorder as you can buy. But having said that, even a low-end recorder these days can provlde a sufficently good recording (if fed from a good mic etc rig) as a more expensive one. Maybe side by side comparison via an impeccable playback system might reveal differences, but not many people are going to sit down and do that kind of analysis (or test recording in the first place).