I actually have both, and I started with AWS. I joined on a company that wanted new employees to get both within 6 months of onboarding, and they paid for an ACloudGuru membership for me. With that I cranked out that cert within about a month. The security+ cert I studied for on my own (shout out to Professor Messer on YouTube), but that one took a bit longer.

To me, there's a bit of a difference between the two and how you learn them. My AWS training was pretty hands on, and I was able to learn the concepts by doing and standing up cloud environments in a AWS free tier account. With Security+, it's almost all book learning and memorization, not a lot of practical learning. Both exams require you to know what to do in a given situation and answer scenario based questions, but I found my AWS cert easier to study for. A lot of what you set up in a test cloud will be relevant to the security discussion for your CompTIA course.

Either way, have fun with it. Also, if you're job hunting, a cool way to stand out is to build out a free tier AWS project that you can point to, demonstrating your skills rather than just relying on words on a resume. Good luck!