So, if I go to California with my NY cell phone and dial 911... I get the emergency services of the tower I connected to? Was always curious who I'd get when I'm not near home.
However if you have VOIP, not all VOIP providers support 911 but the ones that do want you to set a 911 address on your account itself, phone number or for a specific Analog telephone adapter - ATA Device from my understanding. I know our cable company provides phone service and the old modem had a sticker warning about VOIP and E911, not sure if the new one does or not since haven't looked at it too much.
If possible, try to use a land line, because the emergency calls are often routed to a different location when made with a cellular phone. This may not be true everywhere, but at least where I live in northern CA cellular calls are routed in such a way that response time can be 20-30 minutes slower than if made via a land line. When experiencing cardiac arrest, the difference in minutes can have a profound effect.
Apps running on the phone have access to your phone's GPS and can get more precise location data, if you have allowed it. Using an emergency app (Active911, Smart911, etc) will provide more specific location data to emergency services, but these are applications that rely on data and GPS to be working and may not work in as many situations as a simple 911 call.
As far as who receives the call, I imagine it is just based on who the tower is preconfigured to forward the call to. If the tower you are connected to is close to a highway, you'll probably get highway patrol. If you're in town, you'll probably get local police.
It's probably best to just stick with 911. That's what calltakers are used to, and trying to route around 911 means you won't get the advantages built into that system (like priority handling, mapping, etc).