Here are the questions I am asked most often:
Is the content and study topics the same?
EC-Council and CompTIA have a different testing styles. The overall objectives are similar but the CEH exam focuses more on the hacking process and attack types. The Security+ will focus on the layers of defense and terminology used most often in data security jobs.
Take some time to review the different types of malware and types of attacks.
Some vocabulary to familiarize yourself with:
Do you need to take both the EC-Council Certified Ethical Hacker and the CompTIA Security+? It doesn't hurt and your resume will look AMAZING. Depending on your role or next career steps, one may be more relevant than the other.
If you are already studying for one, go directly to the other to reduce the info and time needed to achieve both.