The CAT 108 only goes north from McCarren, the 109 goes both north and south; since downtown is north from the airport, make sure you take 109 in the right direction. (As noted these can both be boarded on the ZERO level.)
The CAT can actually get you downtown faster than the shuttle. The shuttles, usually, must first fill-up before departing--this could take 30 minutes; then they drop off passengers at their hotels. (For me, I seem to be the last one being dropped off, no matter what hotel I am staying at)