scythe big shuriken or thermalright axp-140 ? (<7cm height, low airflow, without cpu fan, using only case fans)

Neither is design to be a passive cooler, the AXP 140 should be better since its slightly bigger but at 70mm height and this is your restriction you wont have the option as you would with the Big shuriken since its only 58mm height (i think its with the fan in) so might end up a better option. What CPU are you trying to cool? what will be its typical load? what case you running? how many fans?

interesting, I was not aware there was a version 2 of big shuriken...
but I haven't found any comparison test yet

I know they were not designed to be passive, but they are the best low profile heatsinks under 7cm I could find. Before there was shuriken I used thermalright xp-120

The Big Shuriken 2 has an extra heatpipe and, more importantly, a backplate mounting system instead of pushpins. I wouldn't expect temperatures to be much better, but the backplate will make installation much more secure.