How do carbureted and fuel injected engines compare in high altitude?
Disadvantages of fuel injection:

You need to do a business case.  It's possibly not worth the price.  The Bendix fuel injection system used on the Lyc is a fairly crude (by car standards) mechanical constant flow system, and the specific fuel consumption is perhaps 5-10% lower, maybe, at best, .4 lb/hp/hr vs .44 or so for a carb (cars are in the high .3s, diesels in the low .3s).  Lets be generous and say the fuel burn is 9 gal/hr instead of 10. At 100 hrs a year that's a $500-550 saving.  If you spend 5000 extra for the injected engine, it's 10 years just to break even.  Hopefully the fuel injected option is a lot cheaper than that, or you do enough flying to recoup the extra price much faster.

You prime by pressurizing the system with the fuel pump (using the mixture) to inject fuel pretty much where the primer would be on a carbureted engine; so far so good, but it's a somewhat more finicky procedure and easy to flood.  

There's a little bit of a pucker factor issue because you have a high pressure fuel distribution system snaking around the engine (yes there are primer lines on a carb engine but they aren't pressurized) so there is a higher fire risk due to a fuel leak (it's the main reason carbureted engines are always updraft - nobody puts the carb on top).

When the engine is hot and sitting on hot day, you can get vapor lock in the distribution manifold and lines, sizzling away like a pan of bacon in the plenum of the cowling, making the engine really hard to start.  If you're on floats drifting away from a dock after pushing off and frantically trying to start the dang thing before you drift into the rocks, it becomes a big deal.

My personal opinion is the fuel burn reduction is not worth the costs, extra failure modes, and loss of simplicity and I prefer carburetors, for simple, low speed airplanes at least.