Does brown rice or white rice expand more when cooked?
I'd say the answer will depend a lot on the exact type of rice, as well as cooking method, and how much you might "fluff" it afterward.  I've seen internet sources that claim brown rice expands more, and other internet sources that say white rice expands more.

For a more precise measurement, I went to the USDA food composition database.  There you can find measurements of nutrients by volume for cooked and raw rice.  Although volume measurements are difficult for things like cooked rice, I figure if there's any resource that attempted consistency in measurement, it's probably something like this.

Anyhow, what I did was compare the calories listed for 1 cup raw vs. 1 cup cooked rice in various instances from the USDA nutrient list.  I assume there aren't a lot of calories randomly lost during cooking (or at least any minimal loss is at similar rates).  Note that the standard USDA preparation seems to be to cook until all water is absorbed (for example, in data sheet here), rather than methods like boiling in excess water and draining, which could result in more nutrient loss.

So, by comparing the calories per cup in raw vs. cooked, we can get a sense of the relative expansion of each variety of rice.  Here's the data for calories per 1 cup portions, along with my calculated expansion ratio.

Brown rice


Long-grain: raw 679, cooked 248 = ratio 2.74
Medium-grain: raw 688, cooked 218 = ratio 3.16


White rice


Long-grain: raw 675, cooked 205 = ratio 3.29
Medium-grain: raw 702, cooked 242 = ratio 2.90
Short-grain: raw 716, cooked 266 = ratio 2.69
Glutinous: raw 684, cooked 169 = ratio 4.05


Bottom line is that the shape and type of rice grain seems to matter just as much as whether it's brown vs. white.  Again, there are bound to be inaccuracies here, so I'd only take these figures as estimates.  But there doesn't seem to be a significant trend that brown rice always expands more or less than white.