What are the key things to hone in on when comparing two ideologies?

This would completely depend on the question. However, there are certain big areas to focus on when comparing ideologies. Begin with the ideology's attitude to human nature- is it inherently pessimistic or optimistic. For example- Socialism innately trusts human nature whereas Fascism believes it to be selfish. From this you can go onto the next big talking point- role of government. And from there onwards you can discuss economics, law and order etc. (or whatever would be relevant to the question).

For more specific ideologies (such as feminism and ecologism), rather than discussing human nature you should first define what the ideology's concern is. From there expand on how that affects their attitude to government, economics etc. So you can end up with a structured comparison which is thorough about an ideology's methods and motivations.