Battery selection for a robot
It depends on your robot and the competition.
If speed is part of the competition, you are much better going for the 300 mAH unit. It's likely that the 300 mAH battery will weigh in at about 20g or less and the 1000 mAH at 60g or more. Carrying 3 times the weight will impact your speed and potentially balance. Most Quadcopter Li-po 300 mAH packs are rated to 30C so should be adequate for your purpose.
Having a fully charged battery for each run you compete in is good practice ...if you get three runs, have 3 * 300 mAH packs.  

Arrange the plugs on your robot to allow two batteries in parallel, and do your tuning and software updates using a large (5000 mAH) battery on longer leads (or you can connect a battery charger). When you are ready for competition simply plug in your 300 mAH in parallel to the big one.....unplug the big one just before you are ready to run.