The Android Market isn't as big as the App Store, but with about a quarter of a million apps, it's still huge. There's only been one application - RoadTrip (a fuel economy tracker) - for my iPhone that I haven't found an equivalent for on the Market. But there are plenty of alternatives, so I just downloaded a different highly rated app and that was that.
Preference is trickier. There are definitely apps that I had for my iPhone that work a LOT better on Android. What'sApp, for instance. The iOS client for What'sApp was terrible, and the Android version is leaps and bounds better. Same goes for google maps...it's lightyears ahead of what came bundled with the iPhone. But other Apps I've downloaded were better on iOS. It really all comes down to the developer, and how they ported the app to each device. In general, though, I'd say that most things are just about on par, so you certainly won't feel like you're getting cut-rate versions of apps. Most of the major apps - Netflix, Skype, Pulse, etc. are nearly identical.
I live in Maine and I am an AT&T customer. The international version of the Note has 3G and HSPA+ speeds for AT&T's network. When my Note arrived, I popped the microsim out of my iPhone, made a sim adapter (i traced a friend's regular sized sim and then cut it out of thin plastic), and slid that into the Note. Then I updated my settings as recommended in this forum, and I was up and running in about 3 minutes.