My experience in dealing with the general public is the questions usually go like this:
- "Is it real" or "Is it an original"
- Often followed up by "does it have a 427?", sometimes "does it have a 427 side-oiler?" or, infrequently, "does it have an FE?"
It appears most people who admire Cobras but who don't own one are most interested by whether it's an original or a replica, then by the type of engine that's installed. There is a clearly a mystique or reputation around the 427 FE engine in the minds of many, particularly the side-oiler version of the engine.
I'm not suggesting in any way that opinions of non-owners should sway the decisions of those who actually own one, but many building or buying Cobras share that same philosophy - the 'bad a** 427 Cobras' that created the brand image had FE engines so that's what they want. No argument here on that choice, and 50+ years of development since FEs first started rolling out the doors have made it possible to build better engines than Ford built.
Having said that, 385 and Windsor engines are both common choices as well. The former has the advantage of big displacement, HP and torque at a (relatively) low cost - albeit with a bit of a penalty in both bulk and weight. That's what I have and the torque makes it fun and easy to drive - especially just cruising around. OTOH, once most people hear it doesn't have an FE they're less interested - even if it is a better engine in many respects (e.g. canted valves, really strong bottom end, huge CID potential).
Windsor engines are obviously the smallest and lightest form factor of the three (all things being equal like block and head materials), and 427 CID and larger displacements are available. Even Ford produced a 460 CID crate engine on the Windsor platform. If an owner wanted to be able to honestly answer 'yes' to the "does it have a 427?" question, then that could be done with a Windsor. Routine maintenance s/b easier with more room around the engine and the lighter weight helps in balance and handling.
Coyote engines obviously have huge potential, especially for "out of the box" power levels, but they're wider than 385 engines (though obviously much lighter). The Coyote just doesn't do it for me in a Cobra - though one would be a blast in the right car (e.g. FFR '33 Hot Rod).
If I was building new today I'd go Windsor, most likely in the 408-427 CID range, primarily for weight and size reasons.
As to a non-Ford powerplant, that's just wrong. YMMV