Besides that, both types of boards can have a variety of unofficial/official power structures, consideration of the welfare of non-constituents/non-shareholders, and varying degrees of competency.
This isn't to say that any type of governing body has arbitrary properties. Predictable inequalities exist.
Governments can be investigated by legislators, executive agencies, and courts, as well as subject to document requests (e.g., FOIA in the US), and journalists. Governments themselves don't typically operate as an advertiser in the press, hence, putting purse control over coverage.
Governments are typically more long-lived, and hence have longer-lived planning and concern horizons, than corporations.
It's not perfect, but political power is a check on corporate or financial power, one of several.