For the AT MAX I am going to side on the "relic" side of best operation. The AT Max has better gain, better sensitivity and better depth in various types of soils. It incorporates the true all metal mode, with a probable ID notch on the fly. It is more sensitive to iron, again, a feature geared more towards relic hunting. Those same features allow it to be used as an excellent water machine too. It is also a nice coin hunter, to get those deeper coins.
The AT Gold has the highest operating frequency of 18 kHz, most efficient for small gold nuggets. It also has the "ground balance window" which allows the machine to operate in a variety of ground conditions, so it does not have to be constantly ground-balanced for compensation. The AT Gold also utilizes the true all metal mode for best depth and sensitivity. The manual states that the AT Gold is not recommended for salt water usage.
The AT Pro has the most balanced utilization of tones, including the iron audio. It lacks the true all metal mode, for depth, but is the best machine for those who prefer to hunt using mostly tones, making it a great choice for coins, jewelry, relic hunting and water hunting.
All the AT Series have various coils both DD and concentric in different sizes to help focus in personal target type, depth, target separation and ground conditions. All the coils can be used on any AT Series detector.