In this work, we study the interplay between triangularity and micro-tearing turbulence using linear and nonlinear flux tube GENE simulations. We consider scenarios with negative and positive triangularity (PT) plasma shaping taken from existing tokamaks (TCV, DIII-D, MAST-U and SMART) and EU-DEMO. The study of all these tokamaks reveals a coherent picture. Negative triangularity (NT) geometry is more susceptible to micro-tearing modes (MTMs), which, when present, make transport much worse than in PT. At sufficiently large β (the ratio of plasma pressure over magnetic pressure), magnetic shear and ratio of electron to ion temperature gradient, all the scenarios with NT are dominated by MTM turbulence. In contrast, the corresponding scenarios with PT remain dominated by electrostatic turbulence and MTMs are subdominant or stable. We observe that conventional tokamaks usually operate in a parameter space far away from the onset of this MTM-dominated regime in NT, thus preserving the beneficial effect of NT on turbulent transport. In contrast, spherical tokamaks (ST) operate close to this regime and may ultimately exhibit worse transport at NT than PT. We find that lowering the magnetic shear in STs can preserve the beneficial effect of NT on electrostatic turbulence and prevent strong MTM transport. Finally, linear and nonlinear simulations reveal the reason for stronger MTMs: the magnetic drifts are faster in the NT geometry.