The 501 and 450fx are similar enough that it will come down to the more subtle things.
As others have noted, the big things are similar:
Electric start
Wide ratio trans
Fuel injected
Decent electric output
Either way you will likely make some mods, but just depends on how much. For example, the stock 501 thermostat will probably get you by with a engine shroud,. but if you are going to do an avid or thermobob stat no matter what, then the 501 having a stock thermostat is moot.
Airbox location might be something to consider. If you open up both boxes to avoid snow issues, intake noise is increased significantly. Some have reported the front-facing yami intake is louder for the rider due to location, and requires use of earplugs. That alone might be the deciding factor for a person.
The power bands are presumably a bit different, but my question is "To what effect?" If the max hp is similar, then one revving higher than the other in and of itself makes no difference (unless you start talking turbos, but that is an entirely other conversation).
I don't know exact power curves and horsepower for each, but for the sake of discussion not necessarily related to these bikes but more to the discussion of "450 or 500", if two bikes made the exact same max hp, but one at 9000rpm and one at 11000rpm, what is the difference as it relates to snowbike use? You would likely just find yourself operating that bike/engine near the rpm that it makes max hp. I think its more more important what the hp curve and torque output and curve are AROUND max hp and not only at max.
Quick revving engines change the feel as well. It feels like the 450 revs faster which makes sense compared to a big bore, however, I've never read documentation that shows the details. Maybe the 450 revs faster (meaning rpms climb faster when measured against the clock), but since it has a wider rev range and needs to rev higher to get to max hp, does it all wash out since it has more rpm to cover to get there? I have no idea, but what if it takes a 450 the same amount of time to rev from 5000 to 11000rpm as the 500 engine from 5000 to 9000rpm. If that is the case, again, how does that effect use in a snowbike? It would be interesting to see documentation.
Same with a "snappy" engine. Some engines feel snappier or "faster/quicker" but does that mean they are? Nope. It is just the seat-of-the-pants feel what we experience from a particular engine tune and power delivery. A weak midrange and/or super strong top end power make an engine feel snappier and quicker than it is. An engine with an extremely linear power delivery might feel slower, or even boring, but could actually accelerate quicker than a snappier feeling bike. Seat of the pants feel can be very deceiving, but in the end might be more important to a rider than actual numbers. Personally, unless riding for a competitive race, I think there is more value in a a bike/engine that "feels" faster even if it is not. Hey, if not in a race, what do we ride for? The feeling! So to me, the feel trumps the actual numbers anyway which means trying a bike to get the feel for it.
Lots of ways to think about it and without riding both back to back, you probably couldn't tell the difference anyway. The wide ratio vs. close ratio transmission probably makes more of a difference than engine at that point.
I guess that got a little philosophical and asks more questions than it answers, but all fun to think through. Ha.
The other thing you might find is, depending on how much you mod the bike for winter use (stiffer fork springs, intakes, etc), you might find it a real pain changing back and forth a couple times a year and end up realizing that it's better to have a dedicated snowbike bike and dedicated summer bike as what works best for each, depending on the person, can be vastly different types of bikes.
Bottom line, either one will be a blast, but if you really want to know what is right for you, you'll need a bit of seat time, even briefly, on each to compare engine feel and other things that no one can decide for you like noise output, chassis ergonomics, etc.
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