When I last participated to ATLAS, working in the Trigger & Data Acquisition group, ATLAS had 3 levels of trigger: the first was hardware, the others were software.
Regarding the first level, software was not an option due to the extremely high bunch-crossing frequency (40 million times per second).
The difference between the 2nd and 3rd levels consisted of data availability (region-of-interest only for 2nd, full detector for 3rd) and algorithms permitted (light algorithms for 2nd, full reconstruction and advanced analysis for 3rd).
The maximum allowed output were, IIRC, 100 kHz for 1st level, 3 kHz for 2nd level and 100 Hz for 3rd level.