Can't help you with the waiting part of your question since back in the US I never owned a carried-provided phone but always free-market alternatives instead.
What you'll lose:
* The entire Nokia/Lumia-Suite of applications, including Lumia Camera, Lumia Panorama, etc.
* The entire HERE-Suite of applications, including HERE Maps, HERE Drive+, etc.
* The Nokia ringtones and notification sounds (probably not a big deal)
* Certainty of quick updates since Microsoft now provides you with both hard- and software
At least part of the Lumia-Suite will be included in Windows 10 so you might get that back. There's no way of telling how well HTC and Samsung are going to handle the upgrade to Windows 10 but from experience with both companies I'd say chances are slim to null. With Lumia devices at least Microsoft has clearly stated that all Windows Phone 8 devices will receive the update but then again this might still change in the coming months. However, given that you're on Verizon I wouldn't expect to receive any updates ever once you've bought the phone anyway.
That's about it I guess, can't think of anything else.
I don't use the Nokia apps too often. Sometimes I'll use Lumia Camera but for the most part, the default camera app is good enough for me. If I lose HERE Drive+, what's the default GPS app for Windows Phone? As for updates, I'm in the developer preview so I'll still get Windows 10 hopefully.