I was looking for rechargeable batteries to power a device I was making, however the high costs of chargers and even the batteries themselves made me want to consider other alternatives. I came across a few mobile phone portable chargers which provide enormous amounts of energy (15000+ mAh) and charge very fast despite costing less than £15. I was wondering whether these power banks would be of any use for powering an arduino and a few motors instead of rechargeable batteries. Are there any (operational) differences (apart from the cell chemistry and voltage) in the two?
No, there isn't. For most, they are a single Li-Po cell with a built in charging circuit and boost output, with auto cut off. They will boost to 5V typical. There are also larger 12V ones, or ones that can do both.
Some newer ones have auto-shut-off if they don't detect a significant load. That may be an issue. Stick to the dumb ones.
These are ideal for your needs.