Deck stair landing question

I'm resurfacing the deck on a 20-year old D.R. Horton home. The original deck was cedar but all the joists are in good shape so I'm just resurfacing it with composite.

I was also going to re-use the stair stringers which are also in good shape. But looking at deck designs it seems that the standard way of constructing stairs is to tie the stringers in below the rim joist such that the top step is below the deck level and you make one more step up to the deck level.

The old deck was made such that the stair stringers were mounted level with the top of the rim joist such that the first stair was level with the desk surface. This doesn't seem the standard way to do it. I can cut down the stringers to remove a step and do it the normal way but that will require adding additional bracing under the rim joist. Or I can do it the way the old deck was built.

Is there a right or wrong here? I wish I had a photo of the old stairs but I already tore them off.