Most accurate isn't an issue - there's one algorithm for determining position with GPS and that's what all GPS receivers use. Accuracy depends on the number of satellites being received and the weather. (We're talking about billionths of a second of time it takes a radio signal to get from the satellite to your receiver. A cloud can slow that enough to throw the fix off by meters.)
As for starting time, cold starts take longer than warm starts, so it's more a matter of how you use it than of how long it takes to start. (The receiver has to get a full transmission, no static, no missing bits, from at least 5 satellites to get the initial fix, so tree cover, buildings, even electrical noise from surroundings, influence the start time a lot more than which phone you have.)
Typical warm lock time (the GPS was turned on in the same place it was last turned off) is anywhere from 5 to 30 seconds depending on conditions - even for the same phone. Cold start time - you turn it off in NY and turn it back on in Moscow a month later - can be minutes.
(I just tested my Note 3 for a warm start - 17 seconds. That's typical.)