There are many differences between pen style and mini. The primary difference, as you suggested, is size. When the PV was first developed, the designed was targeting a pack of cigarettes (number of "mouthfuls") as his replacement goal. This dictated a certain battery life and liquid volume. The form factor was similar to a regular cigarette, but he couldn't achieve his target in the size of a regular cigarette, so instead he chose another familiar look (a pen) for his original design. When the popularity of the pv exploded, manufacturers discovered that new vapers were looking for a form factor more similar to a cigarette, so that they looked like they were smoking. Thus, the several varieties of mini were born. The pen style still stores more battery life and juice, but in appearance is different enough from a cigarette that it isn't as popular.
Most vapers start with a mini and then "graduate" to some other variation (ego, box mod, Juice Box, etc.) based on the discovery that looking like you are smoking is not as important as actually being able to vape for a longer period of time without changing batteries, cartridges, etc.
Flavor and volume are more directly related to atomizer design (resistance) and battery voltage (3.1, 3.7, 5, 6, 7.4, etc.) The higher the voltage, typically, the more volme of vapor production, however there tends to be a loss of flavor as the juice tends to be burnt, unless the atomizer you are using stays very wet and / or is designed for a higher voltage operation.