How are the opportunities for citizens to participate in the US government similar to the opportunities for citizens in ancient Athens?

A citizen of US has a much better chance in participation.

Explanation:

The democracy of Athens, as loosely as one can state it was heavily skewed for the elite class and they were the ones voting as well as deciding what would be done in their society.

This makes the government very restricted and ultimately in the hand of a few people.

Compare this to US, and virtually anyone who tries and has a certain amount of luck along with a penchant for administration has a chance to contest and win elections in US for some position.

All US citizen are entitled to vote and vote for multiple issues many times a year.