Should I guest post, advertise, etc. on existing sites where users talk about my competitors or should I find new sites similar to my target audience?

The answer to this question is surprisingly pretty simple and it depends on who your target group is.
If it is a subgroup of your competitors' users, then do engage where they already talk about your competitors.
If your target group is people who don't use the product yet, then go where those people are and engage there.

Defining who is your target group, what is the solution your product offers to their issues and how to engage with them is sometimes complicated. I'm happy to jump on a call to help you clarify all this. It will help you in this specific question you have just raised but also in the future whenever you need to decide what to do: it's always all about your target group and their needs.
Serena

I actually think your asking the wrong question. You should first focus on what differentiates you company from your competitors, otherwise your just another company to the prospective client. Why should I do business with you vs. your competitors? If you have a solid value proposition that answers this question then you should advertise with everyone else, if not, find other sites with less competition.

While I think it is important for your company and its offerings to stay visible amongst competitors for solving the same or similar problem for the user in your space, I don't think it should be the ultimate focus for customer acquisition. Why? If you are consistently benchmarking amongst your competitors to drive new customers, prospects might always be feature and cost comparing between the players in the market vs. recognizing the unique, distinguished value your product or service brings. Then it just becomes a race to the bottom.

I would go after websites that have some overlap for your product and service and position that one, unique factor that your competitors don't have. It might, like you mentioned, require more learning curve but if you can hone those skills in selling and onboarding - I believe you can affect a more positive outcome.

Good luck! If you found this answer resonated with you - happy to followup with a call.

Thanks!

Why on earth not do both? Find a way to measure the success of each approach. Compare. Adjust your time / expenses accordingly.

That's the empirical approach. Good enough for hard science. Good enough for marketing.

Why pretend the answer lives inside somebody's brain? Your answer is out there in the world, untested and undiscovered. Go find out what actually works in practice.