There's not big differences between those two scenarios.
Contemporary fluid dynamics bearing drives can run 24/7 for years without any problems or degradation. But the running drive is hotter and secondly, it is more sensitive to any mechanical or electrical shock. So, if your drives run in a room where's optimal cooling, no vibrations or sudden shocks, plus good quality power supply then I don't see there any problems. I have several cheap desktop class ATA/SATA drives which are running 24/7 continuously up to 2 years so far and no single problem with them. But they are pretty rarely accessed, so they get very low seeking load. Usually just the active 24/7 seeking will kill the drive mechanics (actuator, heads) and may also make sudden head crashes into platters.
HDDs also live well years with power plugged off and drive stored somewhere in safe place. Although there may occure situations where drive powered on after long standing on shelves will not start up anymore (motor/bearings "freezed" or smth). Also, every spinup/spindown process stresses the drive in some degree (although contemporary drives are designed to live 50,000+ of such cycles), there may be even electronics one-time burnout caused by high startup current. Still, these problems are more theoretical and I have not experienced them so far. And I have drives stored (powered-off) from 15+ years ago which could spinup and read data without any problems today.
About specific HDD model selection for such a use - look for several topics on SR forum here, even in couple of last days there have been two or three of them...
FDB bearings are least consistent when first being spun after a down time of about thirty days. Safest bet for FDBs is if they are off for any extended period of time, power them but do not access them for about 5 minutes of spin time so as to optimize bearing fluid viscosity. I think maxtor had a widespread problem with early FDB based models.... something about it causing platter movement on a particular axis... can't rmember but I'll post back in a couple of days when I find the white paper I was reading.