Air cooled heatsinks - horizontal or vertical fins?
The difference should be pretty dramatic, due to the specifics of free convection airflow.

When the fins are placed vertically, the air flows along all fin surfaces, hot air rises and provides the best possible heat exchange. The active surface will be on both sides of the fins, and along the surface of the baseplate. So the effective heat exchange surface is the the entire fin surface, which is 5-6 times bigger than the surface of the heatsink's baseplate.

When the fins are positioned horizontally, the rising air has to flow across the fins, with pockets of stalled air between fins. So, effectively, the active surface of the heat sink will be of the size of the heatsink's baseplate. Of course, there will be some escape of hot air from these pockets, but the rate of movement is much slower than when the fins are vertical, with no obstruction for air to escape. So the thermal impedance of a heatsink with vertical fins will be 2-3 times better (smaller) than when the fins are horizontal. 

Also please note the distance between fins - the fins are wide spaced, as compared to forced-air sinks. This is done so that the boundary layers around the fins' surfaces don't overlap along the space between fins, and the heat exchange is optimal. A heat sink with tightly-spaced fins would behave as a solid brick under unforced air conditions and won't be very efficient. 

ADDITION: The link supplied by Janka in the comments contains simulation data in support of my hand-waving explanation:



ADDITION2: Note that the above difference was modeled assuming the surface being bare metal with emissivity of 0.1. The effect of orientation of this heat sink relative to gravity field will be offset by the fact that about 1/3 of heat flux will be emitted in the form of radiation if the sink is anodized or painted black, which will make the surface emissivity to above 0.9. And the radiation is omnidirectional. The other factor that would diminish the effect of orientation is the material of the sink and construction of fins. Thin fins don't conduct/transport the heat well from baseplate to edges, and the edges will have less temperature difference to ambient, be less effective. Copper will work better and make more difference. There are several factors at play in different directions, so the exact effect of orientation is difficult to calculate, and only a sophisticated software as FlowTherm or similar can give a trusted result. Or an experiment. Still a factor of 2 will be a good ballpark estimate.