SR Flip-flop with 2 npn transistors - initial state
I suggest you attach an ammeter to each LED leg (one at a time if you only have one) and it might become clear what's happening.

In short, the green LED will have a higher forward voltage, so the red LED will flow more current (resistors are the same value) and turn on the green LED side's transistor first.

If you use the same color (preferably the same part number, from the same lot) it might become more "undefined" (or not, given part-to-part variations.)