If you know electric stuff, this will help: Pressure is like voltage, air flow is like current. A pressure difference in the two balloons is like a voltage difference. The tube and valve connecting the balloons has a "resistance" to air flow. The air flow between the baloons will be $F = (P2-P1)/R$ where $F$ is the air flow rate, $P2$ and $P1$ are the pressures in the two balloons, and $R$ is the resistance to air flow of the tube and valve between the two balloons.
What is $R$? Exercise left to the reader. Given what I'm telling you, you can think of a few ways of measuring it, and even determine what its units are. But I will point out the following:
- $R$ is higher for a thin tube, lower for a wide tube.
- $R$ is higher for a long tube, lower for a short tube.
- If the valve has large uninterrupted room for airflow through it, it won't increase $R$ much, if it is more restrictive than the tubes, it will dominate $R$.