Jim, the GX Hondas are pushrod overhead valve, while the GC Hondas are overhead cam. The GX engines are rated as "commercial", while the GC engines are rated as "residential". Essentially, the GXs are intended to be highly reliable for a long time, and easy to overhaul. The GCs are intended to run just about as sweetly as the GXs, but tend to be a bit less reliable and are a pain in the backside to overhaul. The pushrod engines have detachable cylinder heads, while the OHC engines have integral cylinder heads and the overhead camshaft is driven by a rubber belt.
There is also a sort of halfway-house: the GS is sometimes advertised as "semi-commercial", despite having an overhead camshaft. As an extra layer of confusion, after introducing the GX22 and GX32 pushrod 4 stroke brushcutter engines, Honda broke its own rules by replacing them with overhead cam engines but calling them GX25 and GX35. I suspect their marketing department did that, rather than their engineering department.
In home service on a reel mower, the GC160 might give satisfactory service. It should run beautifully like other Hondas, but it might jump its camshaft timing, which is easy to fix but rather annoying if you don't recognise the symptoms immediately. Repairers would probably charge quite a bit to retime it, even though it would only take a few minutes if they knew what they were doing. If it ever needs overhaul (which seems relatively unlikely in residential use) you would curse it roundly. Its carburetor is also a bit harder to clean than a GX one, due to a "cost saving" in relation to the idle jet. Bear in mind that the GC160 is 160 cc and 5.5 advertised hp, compared with the GX120's 120 cc and 4 advertised hp.
