Key differences between solar-cells used for terrestrial and space applications
Triple-junction cells are often used in space applications. The three junctions can be:


GaInP2
GaAs
Ge


Remember that they are also semiconductors -- over time, as they pick up radiation damage, they will deliver less and less power. Beginning of life efficiency of some of space models can range above 26% or so as well. End of life degradation may be published online, but I'm not sure how public that info is.

Bypass diodes are also generally present to prevent a single cracked or damaged cell from ruining an entire string. At orbital velocities, a tiny piece of dust / debris can wreck a cell, not to mention the unfortunate possibility of launch vibration / G-forces cracking a cell in an array on the way up.

System level design considerations could include (not at all a complete or exhaustive list):


"Layout" / topology -- how many in series / parallel. Higher voltages induce different design designs / considerations 
Pointing -- do the arrays move? Does the entire vehicle move? Solar is only useful if you minimize cosine loss. Some vehicles are decommissioned by going into a flat spin with the arrays 90 degrees to the sun.


Energy storage -- generally solar-based systems need to shove power into a battery to continue to operate during eclipse / darkness. This is of course a discussion that is much more complicated, but folks use all sorts of chemistries in orbit.



SMAD III has a good chapter on power systems for space vehicles.

Also, as W5VO mentioned in his comment below, every gram and every square meter counts in spacecraft design. If you are spending mass and area on solar cells (plus the mechanisms to unfold and articulate those arrays), you want to make sure you're making the best out of every single photon that touches them. There's a great comic I'll try to find that shows a spacecraft as designed by various subsystem owners -- the power guys want all arrays + batteries, the comm guys want a giant dish, the controls guys want a huge gyroscope, etc etc.

Here are some popular cells that have considerable flight heritage.