Which would turn to soil faster

Neither, technically speaking. ;) Composting doesn't result in soil, it makes an organic amendment to add to the soil. Soil (dirt) is composed of sand, rock, and other minerals. Just a point of semantics to some but an important clarification for those new to the composting process, ok?

What browns bring to the process is balance. Carbons (browns) are required to both control the timing/rate of the decomposition process, balance the pH of the end product, aid in the retention of the nutrients as well as providing additional nutrients of their own, and to control the moisture and odor problems associated with straight greens.

Which would turn to soil faster: a bin full of just grass that is turned frequently, or a bin filled with grass and leaves that is turned frequently?

Neither will turn to soil but the latter (grass and leaves) will turn to compost much faster. A bin full of just grass clippings will never turn to compost in the usual sense of the word so that is the "downside of just having grass in there". What it will turn to is a sloppy wet, stinking, glob. ;)

Much of this is discussed in the composting FAQ's here as well as several discussions on how the composting process works. There are also excellent scientific-based discussions on how the process works on the web. I have linked one of them below.

Good luck with your composting.

Dave

Here is a link that might be useful: How Composting Works

Browns bring cellulose and lignins. Both are carbohydrates (C-H-O).

Lignin in particular is tough to decompose. Some species of fungi manage it. The woodier something is, the more lignin it has. So, adding browns (1) promotes the growth of organisms that would not find your pile attractive otherwise, and (2) it also provides a "slow release" carbon source.

1. There is no "stupid" question, just a question someone feels stupid asking and they should not. Questions are how we learn.
2. Browns, or high Carbon material, are the food source for the bacteria that digest organic matter. They need the Nitrogen for protein to make their bodies able to digest the Carbon, but the high Carbon materials also provide that majority of the plant nutrients.
3. A pile of a single type of organic matter, grass clippings for example, would eventually be digested and while some would smell bad, and that indicates nutrient loss, eventually it would be organic matter, not soil, to add to the garden. When composting a mixture of material is always better.