Strange-looking FM transmitter circuit
Concerning the radio-frequency oscillator, both circuits are the same. Components that affect frequency are the same too:


C4 of circuit 1 (10pf) is equivalent to VC1 of circuit 2
C5 of circuit 1 (10pf) is equivalent to C2 (4.7pf) of circuit 2


As you have noted, the antenna goes to different places in each circuit. Both places offer a radio-frequency signal. The emitter is a lower-impedance point. Attaching antenna there likely causes frequency to shift less than attaching to the collector.

A half-wavelength antenna wire at the collector would be appropriate.
A somewhat shorter-than-half wavelength antenna would be appropriate at the emitter.