Hollywood or tight installation is more common in my area of Northeast/Mid-Atlantic.

One of the downsides of tight installation in my opinion is that your stairs will have Thousands of staples in it as it is typically installed. So the carpet itself will have thousands of staples in it.

I just did stairs in a waterfall installation. The carpet is old-school velvet cut wool, just about as far away from trends as you can get, and I had it installed waterfall style and there are no staples in it at all. It's installed completely with tackless. I actually like the look, I think it's simpler than having the steps outlined. The installers said they rarely do it this way right now.

I find some carpets lend the selves better to one or the other , Waterfall for sure leass foramal looking . What doe the carpet person advise that usually is the one they are best at . We had I think hollywood on ours when I was akid but it had rods where the rider and tread met . Maybe show us your home style and the carpet .

I don't know that it's necessarily less formal, because most good persian runners are installed waterfall so you don't destroy the rug in the process. I think the formality depends upon the rug. I think the wool velvet cut is much more formal than a synthetic berber, but berber usually gets installed Hollywood.