Money is power. So to answer your question literally, if MY taxes went up, I would not have more power, but if the rich's did, I would because they'd have less power.
If taxes go up on everyone, the rich are still the ones that manipulate the government, but now they have control over more tax revenue. If taxes go down for everyone, the rich are still the ones that can manipulate the government, but now the government has less revenue and can't cause as much damage.
This is absolutely false, especially in the US. Progressive tax brackets, breaks for the rich, and targeted changes for capital vs. income, deductions, etc. are the norm. Tax rate change is _always_ selective.