In many important ways, we cannot give a generic answer to this question. There are many ways in which “it depends” would be the answer.
First, it would depend on the degree to which the monarch ruled the country. There were different kinds of monarchies, with some being absolute monarchies and others sharing a great deal of power with their parliaments. In the former, our lives would be very different in that we would not be likely to be allowed to engage in any real form of political activity. However, in the latter, we would be allowed to do things like voting for our representatives.
Second, it would depend very much on the particular monarch. If we lived under a monarch like Nicholas II of Russia, our lives would be very different than if we lived under Frederick the Great of Prussia. Frederick was a much more enlightened ruler and life would probably have been much easier and more pleasant under him than under the more autocratic Nicholas.
The only answer that would be true in all cases is that we would have less political input. At the very least, we would have a chief executive, the monarch, in whose selection we had absolutely no say. That would be different from our current lives even if the monarch were enlightened and respected our rights.