So, to a point, I feel like I am probably a bit biased because I basically earned my stripes in SEO from SEMRush. However, I'm going to try to make this as unbiased as possible but I can't promise much. 

It actually feels like the question between Answer the Public vs SEMRush is a bit strange. Answer the Public is specifically a keyword planning tool that is mostly a research tool to see what kind of questions people are asking. SEMRush is...kind of everything. 

You see, SEMRush doesn't just tell you what other people are searching. It gives you hard details about the top length of competitors, the competition levels for keywords, as well as the latent semantic index words people use.

AtP? Well, they can compare keywords but it's nowhere near as powerful. If you're looking for an all-over tool, there's no comparison. SEMRush is boss. 

If you talking about the comparison for keyword research solely, then both. SEMRush gives you great data on main searches with extra data such as competition and search volume. AtP is great for looking at extra keywords, or questions that you could utilise for stategies such as answer boxes. 

When we do keyword research for a client we generally use a lot of different tools. SEMRush atp are two that we use often but will also look at Adwords data and Google Search Console. This way we can find the most amount of keywords and topics that clients can use for their digital marketing strategies.