LUFS and dynamic range are two different things, though the latter is related to peaks somewhat. Most loudness measuring tools will tell you about dynamic range.
While LUFS is designed to keep things sounding "the same loudness" there is no doubt in my mind that other factors impact how you hear something, not the least of which is how we hear music, its dynamic range, the things reproducing the sound, and if speakers (vs earbuds/headphone), the space being heard in, as well as the content and where the measured "loudness" is coming from in the music.
I like to start with dynamic range and keep an eye on that, because if you lose that, and want/need it, getting it back will take some unwinding and can cause revisiting a lot of decisions you thought you'd made already. LUFS only matters when you go to the "mastering" phase, really, but it's good to make sure you've not already shot past it in the mixing step, because then you're going to have a different problem, and probably have to go back to visit dynamic range again. The peak is, I suppose, less important, but comparing where you're at with that along with LUFS will really tell you whether you've left much tweaking room after the mix is done. And, maybe you don't need it, but a little bit might be appreciated.
If I said -6dB anytime, it was probably something I read
. But, it's not a horrible place to be if you've got a lot of dynamic range and at least that many dB of LUFS to spare, IMO.