Have taken taxi to Harrahs from the airport many times over the years, never told the driver what route to take, never got long hauled. Traffic is wicked in the afternoon and can lengthen the time and cost regardless.
Airport shuttles are one price ($7.50 per person to any Strip hotel) but you don't sweat being long hauled or the effect of traffic. The downside is possibly a little longer wait for the shuttle to fill up enough for it to take off (in our experience 1 - 15 minutes). And your ride includes cruising the hotels of others on that shuttle (which can actually be entertaining). You could be the first or the last drop-off or somewhere in between. Also, the shuttle drop-off spots are not necessarily at the front door, depending on the hotel. But overall, we prefer shuttle to taxi FROM the airport.
For hotel TO airport we do taxi, as the shuttles are not that dependable on pick-up time...you definitely can't cut it close to your flight time.