Bulbs will glow brighter when connected in parallel. The battery will run down faster if the bulbs are connected in parallel.
Work Step by Step
For two or more devices connected in parallel, the voltage is the same across each device. Each bulb "feels" the full voltage of the battery and glows brightly. However, for two or more devices connected in series, the supply voltage equals the SUM of the voltage drops across the devices. Each identical bulb "feels" only half the voltage of the battery and they do not glow as brightly. The 2 bulbs in parallel will draw more current, glow more brightly, and therefore drain the battery energy more rapidly.