Ach! I'm busted.
G10 and micarta are both composites. They consist of reinforcements encapsulated in resin. Both are very strong.
The term "Micarta" is a bit more generic than the term "G10". G10 is specifically layers of glass fabric embedded in epoxy resin. Micarta can be made of one of several materials embedded in any of several resins. Both are relatively impervious to water or chemicals.
Here is some information on the properties of G10 and why it is called G10:
http://www.bladeforums.com/forums/showthread.php?p=4245397#post4245397
markksr quoted some other info as well.
G10, being layers of glass cloth, has its strength in the direction of the fibers because it is the fibers that provide the strength of G10. Since G10 is usually laid up as flat sheets, that means the greatest strength will be parallel to the flat. G10 was designed as material for circuit boards. The specification that defines it is pretty open as to physical properties that knife folks are interested in. G10, being made of epoxy will degrade on the surface if it were left in direct outside sunlight for a few weeks. (surface turns chalky. That would be the resin starting to break down from ultraviolet radiation exposure.)
The reinforcements in Micarta are cloth or paper (and their variants) instead of the glass fabric found in G10. Micarta can have more strength in the other directions aside from that of the fibers because of the nature and of the reinforcement fibers. Micarta may or may not be sensitive to UV depending on what resin was used. It's somewhat denser than G10. Micarta covers a lot of materials, so it's hard to give specific data.
For knife handles, either material is stronger than any force you are going to apply to the blade and the difference is more in texture and appearance than anything else.