I have used both...in Texas and other southern states. If you are trying to fight the heat, the inside screens pale in comparison to the external shades. Best is to use both, but for thermal protection, if you only invest in one, I recommend external.
Of course the down side is that they are more difficult to install, and you have to store them when not in use, which could translate to less use to avoid the hassle.
2013 Fleetwood Discovery 40G, Cummins ISL,Freightliner Chassis, Allison 3000.
2009 Jeep Wrangler Unlimited Toad w/ Blue Ox Aventa tow bar and M&G Braking System