I have direct experience with one of the mentioned machines, and indirect experience with the other two. By that, I mean that I talk frequently with owners of the two other machines. I will have to temper this answer to the opinions I give are from the sum of the experiences as I have encountered.
The Mazak is an ok machine if it is your first machine and you do not have much of a budget up front. However, it will nickle and dime you to death. It uses up consumables, like nozzles, tips and optics, and the replacements are not as economical as you would like. It requires the most maintenance of the three mentioned.
The Amada is a super machine. It has a very user friendly interface and software package. The basic machine is straight forward design and is robust to do heavy and light work. It is easier on the consumables and gas consumption. It has Fanuc electronics and resonator. I have never been pleased with Fanuc service and their replacement parts are on the expensive side. But Amada may have that covered through their own network. Their resonator technology seems to be fast flow axial CO2 that is RF excited, which is the best current type of resonator.
The Trumpf, to me, is the top choice. It has a RF pumped resonator which delivers a exceptional beam quality. The layout of the resonator is very compact and leads to a smaller overall foot print for the cutting system. The mirror optic delivery system is self adjusting to keep the beam consistent through out the entire cutting envelop. It too is easy on consumables, both hardware and gases. It also uses Siemens electronics which has better recognition around the world. That means service parts are more readily available through out the world.
I would suggest:
Trumpf first, power, compact foot print, excellent service, excellent cutting capabilities. Good software. You might have to stretch your budget up front, but it will pay it self off by process speed and capacity.
Amada second, Good machine and second best power. slightly larger system layout. Good software
One last though, when you buy cutting power, buy the most wattage you can! If two machines are similar price, go for the wattage! It means faster cutting speeds and less waste. It also opens your market up to precision thicker plate cutting. What would a customer in your area pay for 1500mm x 3000mm x 20mm plate cut to +/-.25mm tolerance?