well if you buy a new phone you should definitely go for AGPS, all new models support that.. Just take into account thoough that Assisited GPS actually does use some data over your network, so if it's expensive in your country or you don't have internet connectivity on your SIM/sunbscription it may cost you... The good thing is that you can deactive the A part of AGPS :P
I have actually no idea which chipsets are used specifically, I actually can't say my N5800XM is any faster or more precise than my nearly 3 year old N95... After all those aren't high-end chips which are used, I have worked with gps-receivers that cost around 4000 dollars a piece, which have a tollerance of 30 centimeters, so don't expect miracles from a 20 or 30 dollars integrated chip
The sensitivity is measured in dB so if you can get the specs of the chip;s used you can compare that value to have a rough idea how sensitive they are...