I tend to disagree about the pulsing that is caused by a moving diaphragm/piston being a significant problem, on account that the hose itself acts like a tiny buffer/tank. A hose 6 feet or longer will usually prevent most pulsing of this kind (though short hoses might not prevent this problem).
That said, I still think a tank is absolutely necessary.
Without a tank, when you press the trigger on an airbrush, the pressure in the hose suddenly drops, which signals the compressor to turn on, but then it takes a second for the compressor to re-build pressure into the hose, meaning your air tends to drop suddenly when you first press the trigger, then builds back up, sometimes too high depending on the regulator, then it finally stabilizes and provides a fairly consistent output so long as you hold the trigger down. However, it will also run continuously like this meaning it will get hot faster. This, in turn, means you will need to take more frequent, or longer, breaks to keep the compressor cool. A tankless compressor is ok, so long as you take frequent breaks, and realize that you should never start spraying paint immediately, you have to wait for the air to stabilize before spraying paint; Every single time you press the trigger.
With a tank, all of this fluctuation in pressure happens well above the pressure you are working at. This could be 40-60psi for small compressors, or as much as 90-120+ for larger compressors. So if your air regulator is set at 25psi, you never have to wait for the air to stabilize as there is always a minimum of 41psi in the tank, which allows air from the tank to instantly begin replacing the air in the hose, preventing that sudden drop in pressure when you first press the airbrush trigger. Its a consistent spray the moment you press the trigger.
So long as your compressor can output more cfm than your airbrush uses, you never have to wait for air, or wait for it to stabilize. And, as others have mentioned, a tank gives the added benefit of allowing the compressor to rest between refills , which keeps it cooler longer, which means you can airbrush with less interruptions for longer periods of time, though breaks every hour or so for ten minutes is usually still a good idea (not just for the compressor
).
TL;DR: Get one with a tank, definitely.