If I knew T-Hunters were using Dopplers I'd put my hidden T antenna horizontal negating the effectiveness of heir Doppler use as vehicle Doppler RX antennas are vertical.
Not surprisingly, "no one tool is best for all jobs". I use a combination of equipment here. 4 element 2m beam extends up from my truck out the rear passenger window, gets it about 7' above the truck. Polarized horizontally (but easily changed) works very well to get accurate bearings at distance. (doesn't interfere with the doppler either... which was surprising)
Once the meter comes up, the doppler takes over and bee-lines me right into the neighborhood. A switchable 0-70db (10db steps) attenuator on the omni provides an excellent "you're getting warmer" indicator to complement the doppler. (and can hold its own as the solo indicator) These two bring the vehicle as close as physically possible to the transmitter.
From there, it's on foot with a DF-1 (non ambiguous tone nuller) and a variety of other gear I'm currently testing out such as offset attenuators, dedicated sniffers, loops, and even a man-portable / bicycle-mounted doppler.
Experience with your equipment trumps ALL. The more hours you put on whatever you're using, the more effective you will become. The original group I played with had outright banned directional equipment because of our skill level, yet typical hunts lasted less than 30 minutes. One exceptionally good player didn't even have an s-meter on his radio, he played entirely by ear. An experienced player that has a good understanding of how his gear works will smoke anyone that walks onto the field even with the most sophisticated and expensive kit available if they don't have experience and skill in its use.
If you have several different kinds of gear to use, I recommend trying to do your next few hunts while selecting a single piece of gear to use the entire hunt. This helps you to focus on the subtleties of its behavior, learn how to identify, understand, and overcome its weaknesses, and how to capitalize on its strengths. Don't bounce back and forth quickly between different gear until you thoroughly understand each one and can adjust your gameplay immediately to suit your newly selected equipment.