Very different critters (the speakers, that is)! ;)
Briefly, I have heard both companies products several times at shows and Tidal has been impressive, while ATC has been precise, but not as emotionally involving. I have thought of reviewing Tidal several times, but never ATC. I know I could build kick ass systems with both. The ATC strikes me as a much more in your face speaker, like the Vapor Audio Joule White (reviewed and owned), a laser sharp speaker with outstanding resolution, imaging and transients.
Take your pick/poison:
Tidal: more options to contour sound with outboard amp, cables, etc. but likely much more expensive to achieve superior/gratifying result.
ATC: easier, all inclusive, but fewer options to contour sound and mange issues in achieving gratifying result.
Not overly impressed by the bass extension specs of either speaker you mention. :( I didn't see any frequency response discussion in the specs of the Tidal, and a not too impressive 25Hz -6dB. for the ATC. The Tidal has twin 9" ceramic drivers, so I'd guess it's going to be in the same zone as the ATC, about 32Hz +-3dB. Ok, not horrible, but certainly not what I would call end game for myself in that price category. I would want more prodigious bass if I was going to be chasing The One. That's a pretty harsh, strong assessment, and I do not mean to disdain them, but I am a reviewer and will see weaknesses as well as strengths. I require an ultimate speaker to be closer to 20Hz +/-3dB than 30Hz or higher. For some that is not absolutely necessary, but it is for me.
Even the odd and magical Tri-Art Audio Series B 5 Open Speaker, with open baffle is 27Hz +/-3dB. That speaker system, with it's outboard crossover and attenuated full range I prefer to many of the more expensive box speakers I have reviewed and owned, even ones $15K+
Maybe you can really "have it all," by keeping current speakers and adding another pair of different genre. Perhaps OB, panel, horn hybrid, line array, omni? The variety, done up at a nice sound quality level, is the end game experience for me. :)