Sort of like comparing apples and oranges. Arkansas stones (novaculite) aren't nearly as hard or aggressive as the ceramics used in the Spyderco hones, and the particle/grain size & shape are different also (ceramic particles are usually more acute/hard-edged, so they cut more aggressively). The hard Arkansas stones (translucent or black hard) are known and liked for their polishing abilities. But the difference in aggressiveness means that some steels won't respond to them as easily or quickly as on ceramic hones. Sometimes that's a good thing, though, because the less-aggressive polishing of a hard Arkansas makes avoiding burrs a bit easier. Ceramics are well-known for creating burrs or wire edges more easily, because they are so hard, and demand an extremely light touch.
Either one could theoretically produce a similar finish on an edge. But the difference is in how quickly or easily it gets there, and if other issues (like burrs) are created or avoided in the process.