The LEDs would be lots more efficient than the strobe, which would mean that for the same beam candle power seconds you would have less power going in, and a smaller power supply.
Over a 60 degree coverage cone, you pretty much require 1 lumen per candlepower. So an array of 10 40 lumen Luxeon LEDs (the red/orange ones exceed this) with suitable optics would provide the necessary light output, continuously...and since you need a strobe, you could overdrive them for part of the time and have them off for the rest of the time.
Perhaps a better choice would be the Lumileds Superflux devices. These are 7mm square LEDs, intended for use in things like brake lights on cars (I used them on my bike). They are available with an optic that has a narrow vertical light distribution, but a broad horizontal light distribution, so that not too much light is wasted in directions where it won't be needed. With these optics, you could expect to get something like 10 - 15 candlepower per LED, and the LEDs are only about $0.50 each.
For a drive circuit, I would suggest a current regulating switching power supply. I have a design (
http://www.borealis.com/~winnie/LED_BOOST/index.html ), however it is not suitable for an aircraft electrical system. Feel free to use it as a starting point. Given that an aircraft electrical system might be 12V or 24V nominal, and could spike to higher voltages, I would suggest a design that can tolerate at least 40V on the input, protected with fuses and transient voltage suppression, and capable of producing higher or lower voltage on the output. I would also suggest that the circuit be divided up into at least two sub circuits, each supplying a subset of the LEDs.
-Jon