Is it possible to split-feed a 20 Amp receptacle with one receptacle using 15amp and the other 20amp circuits?
I'll be darned. You can do it.
The crux of the issue is supplying a 20A NEMA 5-20 receptacle (T-shaped neutral) on a 15A breaker.
Since you will only have one socket on the entire circuit, this applies.
210.21(B)(1) Single Receptacle on an Individual Branch Circuit. A single receptacle installed on an individual branch circuit shall have an ampere rating not less than that of the branch circuit.
So a solitary socket on a 15A circuit must be at least 15A.
What if the circuit had more than one socket?
However, if this 20A circuit supplied other receptacles, then you wouldn't have a solitary outlet. Table 210.21(B)(3) would apply, and 15A receptacles would be allowed on a 20A circuit -- but 20A receptacles would not be allowed on a 15A circuit.
How do you breaker this thing?
Because you have a single yoke with two separate circuits on it, the circuits must have common maintenance shutoff. Having two breakers with different values can be accomplished by using individual 1-pole breakers and identified (listed) handle ties.
No, you can't feed a split receptacle from circuits with differently-sized breakers. Here's why:
You can, but you have to meet certain conditions:
The National Electrical Code now requires that the two hot wires in a split receptacle must be connected to a double-pole circuit breaker, so that when the breaker is shut off, the action will automatically disconnect both receptacles. That way, the outlet will be safe to work on.
To my knowledge, handle-tied double breakers with different current ratings don't exist. However, as ThreePhaseEeel points out, you may be able to find UL listed handle-ties for your breaker brand. This would require that they be mounted adjacent. Or you could reduce the 20A circuit to 15 Amps and use the same wire.
Isherwood raises the most relevant point I think, but another issue is that you would only be able to use an outlet (with the tabs removed) with maximum 15A rating. This pretty much negates any advantage of having a 20A circuit (presumably with 12G wire run) anyway.