The observation is basically correct, although the amount of the rewards is of course also influenced by the type of voting (as wakeupkitty wrote).
In particular, however, the effectiveness of the rewards is also characterised by the reward curve. The blockchain uses a curve that ensures that initially increasing SP leads to an overlinear increase in rewards. Only with very high SP (although I can't tell you the exact amount) does the curve flatten out. If you want to know more about this, you should read this detailed explanation.
In any case, someone with 300 SP gets proportionally fewer rewards than someone with 18,000 SP, even with the same type of voting.

and the battery also recovers faster.

This is not true. Filling up the voting power always takes the same amount of time. No matter how much SP a user has. It is always ensured that everyone can vote 10 x 100% per day.