The Antenna are being used for GSM communication(824-960/1710-1930 MHz)
Kindly find the attached picture for more details.

The left antenna (A) has:
1. Smaller in height.
2. More number of small radius turns
3. Small base (magnetic mount)

The right antenna (B) has:
1. More height
2. Less number of turns which larger radius comapared to A.
3. Large base (magnetic mount)
4. Extra Single turn above multiple turns.

Q1: How can i determine the dB gain of antenna?
Q2: If there is no relevant measuring instrument available, can i choose the best among two just on mere physical dimensions?
Q3: What is the purpose of helix/spring in both the antenna?
Q4: What is use of extra helix in Antenna-B?

 

A1: There is free modeling software called EZNEC that you can use for modeling the performance of an antenna.
A2: One of the antennas will always perform better on the lower of the two bands, and one of them will always perform better on the upper band
A3: The purpose of the coil is to add inductance and allow the use of a shorter antenna, or to increase the bandwidth of a given antenna.
A4: Same answer as A3