We have blown in fiberglass in the walls of our build and Im impressed with it. It's my understanding that cellulose has inhibitors for mold and insects. The blown in cellulose that is applied damp should be allowed to dry before covering to be on the safe side, typically a day or two depndent on humidity/weather. The fiberglass is blown into webbed and visquine sheeting stapled to the studs and the cavaties filled through slits. It is extremely dense packed and seals behind electrical boxes, around plumbing, as well as fills voids and cavaties. Some will say that you still get fibers into your house. I find that hard to believe once the wallboard is up and any protrusions such as electrical outlets gasketed/sealed.I haven't experienced that with our application. Out here any holes drilled top/bottom plates for mechanicals/electrical need to be foamed before rocking as part of the insulation inspection.

What kind of vapor barrier is present?

In old work without a vapor barrier cellulose is more forgiving since it can absorb moisture and then release it as vapor.

Fiberglass just forms frost, that can then melt as liquid.

If there is enough moisture to cause issues with cellulose you have bigger problems, and fiberglass is going to make them worse.

There is already drywall up with NO barrier, just some sort of board that my exterior brick are up against. Holes would be drilled in top and bottom of drywall, then they blow it in. I think i am going with fiberglass, it is a proven material that has been around for a while. Plus it's cheaper to do around these parts.

The Brick, as usual, brings up a good point. If you have had moisture issues in the area where you will have the insulation installed, you might want to re-think this. As stated, both will be harmed by moisture. I'm not talking about physical water from a leak(s), but rather condensation issues. If that is a problem, it would probably, since the sq.footage of your project is small, be a better bet to remove drywall from the inside and either install a vapor barrier in the stud cavaties to the outside and sealed, or consider going with a spray in foam insulation that will give you that barrier.