If you've built as many stairways as I have, this is a very simple question to answer. Should I use 2 x 12 or 3 x 12 for my stair treads? Without a doubt I would use the 3 x 12 for a couple of reasons.
The thickness of the three by material gives it some additional strength and that strength could prevent someone from falling through the stairway and getting injured. Visually looking at the 3 x 12 it gives you the illusion that the stairway is safe. Once you start walking up the stairway and the stairs seem solid and well constructed, it takes the illusion and makes it a reality.
If you're walking up a poorly constructed stairway every day, not only is it a safety problem but it takes a little bit of effort as you walk up the stairway, holding on to the hand rail with a death grip, this can easily wear someone out physically and mentally, over time. Stairways should be constructed and maintained with safety as the main priority.
If you've ever walked up and older stairway that was built using 2 x 12 for the stair treads, you probably know what I'm talking about. Walking up and down the stairway, while the stair treads are moving, does not give you a strong sense that the stairway is safe. And of course sometimes the stairway is not.
For example if you have a 3 inch knot in a 2 x 12 stair tread, over time as the wood expands and contracts, the knot can loosen up and fall out of the stair tread, often creating a weak spot in the step. With a thicker stair tread, it will take a little more expanding and contracting to create a weak spot in the stair step.
If you're building a stairway wider than 36 inches, with no center stair stringers to support the stairway, I would suggest using a 3 x 12 or 4 x 12 for your stair treads. 2 x 12 should not be used for stair treads on any staircase wider than 36 inches.
If you choose to use 2 x 12 for your stair treads, select premium grade lumber for safety. Try to avoid using center cut building materials and 2 x 12 with knots larger than an inch and a half. Large knots are one of the biggest problems in construction safety.