Simply put, the amount of liquid and dry ingredients (flour + cocoa, not including sugar or chocolate) in brownies is much much lower than in cakes, so the outside has the opportunity to caramelize the sugars, which the liquid prevents in cakes. In addition, the dry ingredients dilute the sugar to some extent, so you get less interaction between the sugar particles and less caramelization. Both have about the same amount of sugar per weight.
For instance, if I take two recipes from a popular recipe/cooking site: RecipeTinEats and calculate the ratio of water to the other ingredients. I'll leave out the minor ingredients, such as vanilla extract, leavening and salt as a couple of grams are neither here nor there. Note that eggs are about 75% water, and I've assumed 55 g per egg and given the full weight of the eggs (not just the water weight) in the table. Dark chocolate, as the brownie recipe called for contains about 25% sugars.
One for Brownies and one for Chocolate Cake, in grams.
| Ingredient |
Brownie |
Chocolate Cake |
| Flour |
75 |
265 |
| Butter/oil |
200 |
125 |
| Cocoa powder |
30 |
55 |
| Water/ Milk |
0 |
250 |
| Chocolate |
200 |
0 |
| Sugars |
175 |
440 |
| Eggs |
165 |
110 |
| Totals |
845 |
1,215 |
| Water ratio |
0.146 |
0.274 |
| Dry ingredient ratio |
0.124 |
0.263 |
| Sugar ratio |
0.325 |
0.362 |
So, if you reduced the amount of liquid in a cake and reduced the flour (or potentially cooked it lower and longer, you should get a brownie-like crust. Cakes of this sort are called "blondies", and often don't even contain white chocolate.