The only time I have idle issues on my FI bike is when my filter has been packed with powder or the foam filter itself has become soaked from wet snow and then froze. A brush of the filter or scooping snow out of the box fixes the issue and my FI bike runs like a top until it happens again. This issue would be present on stock airboxes for both carb'd and FI bikes. It almost always first presents itself as an idle-death after a long pull or a good bit of throttle blipping through the woods on a sustained run.
With regards to the best/worst bikes to chose from, my opinion is that no matter what you choose, choose a MX bike. Most of them are very close in terms of performance and what you end up deciding on are the little "differences" in the bikes. While I feel that some of the enduro bikes might be a better "all around" bike (for heavy summer and winter use), their biggest trade off is weight and the transmission. The Wide Ratio trans isn't ideal for how I like to snowbike and I feel that the gaps between gears are too large and rob performance. There are a couple bikes that try to bridge this gap and the only one I've seen that does it successfully is the Husky 511 series. 3 Close-Ratio and 3 Wide-Ratio gears giving you the gear precision you want in the woods along with the road speed of the top 3 Wide Ratio gears.
When it comes to carb or FI, both have their issues and both require some kind of aftermarket adjustments. Be it the JD Jet Kit, APT Smartcarb, carb heating, or a fuel controller for the FIs... nothing is purpose built from the factory for our environment yet. I still think that throwing a controller on an FI bike like the Dobeck Performance Gen4 gives you the best bang for your buck. Sure, the APT Smartcarb is pretty damn impressive, but what would be the point of ripping out your FI system to put a carb on it when a $300 controller does the same thing for your current FI? Plus you get the added information of the AFR gauge on your bike so you always know exactly what AFR you are currently achieving in every situation.... I like that kind of stuff.
Regardless, the biggest mistake you can make is letting what bike you get hold you back from riding time. In all fairness, they all get you out there and allow you to have some kick a$$ fun. Pick a bike that feels comfortable to you and buy it. Worst case scenario is you find you like something better, sell the dirt bike in the spring, buy another bike in the fall, and put a new fit kit on. No big deal.