using a 8ohm will be easier to drive from your amp but the power will be divided... say the amp is 300w rms at 4 ohm... connecting it to a 8 ohm will be 150w rms at 8ohm only... and yes the good thing is the amp will run cooler and thus more efficient... and people who run 8 ohm are normally looking to control their sub bass more...

while for the amp to run 1 ohm on a 4 ohm sub... i think shouldn't be a problem if your sub can handle all the extra power... over powering your sub will kill it faster... and your amp will be running much hotter than running 4 ohm... thus also shorten its life span... by how much depends on how you use your things...

cheers...