Insulation deals with R-values. An R-Value can be boilded down to "per cubic inch". That means the 15 inch R-19 fibreglass batting is NOT R-19. It is advertising the R-Value for that THICKNESS. To find out the true value, you simply divide "19" by the thickness (15 inches) = R-Value 1.27. That is a low number.

Solid styrofoam insulation should have R-Value 4 - 6.5 per cubic inch. The cellulose runs in around the 3.5 range. In MI you will want the highest R-Value (per cubic inch) that you can find. In theory, you would need 3.5 inches of Styrofoam (the highest level of product) to achieve R-20 in the walls.

The same R-20 in cellulose = 5.75 inches for the same rating. Check the cost of the expensive with HIGH R-Values to the incexpensive with lower ratings. Find out how much the TOTAL amount of product is to achieve the same R-20 value. That should guide you to the best fit for your circumstances.

So, it looks like I could go with either type, but the key is to make sure to get enough depth of either to achieve the desired R value, correct?

That's about right. There are a few other things you want to investigate such as "moisture resistance" settling properties (blown insulation can have a tendency to settle = loss of effectiveness), costs to achieve the appropriate R-Value; installation costs (does it take a trained professional with specialized equipment or can anyone on the job site install it), etc.