Welcome to the forum!
I would start by saying that, technically speaking, Manjaro and EOS are more similar than they are different. That being said, there are some key differences.
- Manjaro bundles updates into releases, EOS lets updates flow in as packages are updated upstream
- Manjaro has channels(stable, testing, unstable). EOS does not. The Arch testing repo is available but that is not really the same thing as Manjaro channels.
- Manjaro maintains many different kernel versions. EOS generally has versions of the latest LTS and the current kernel available. Other versions are available in the AUR or other repos.
- Manjaro has prebuilt kernel modules for several common drivers. EOS relies on either dkms modules when there are not prebuilt modules upstream
- Manjaro has an automated driver management framework MHWD. EOS has some scripts to assist with tasks like installing nvidia drivers but generally relies on the you to install the drivers you need.
- Manjaro has a kernel management tools which also manage installing the matching Manjaro modules. EOS has a graphical kernel management tool but you need to either use dkms modules or manage the modules yourself.
- Manjaro DEs are heavily themed and customized by the maintainers. EOS mostly ships uncustomized DEs and allows you to customize them yourself.
- Manjaro has separate ISOs for each DE/Edition. EOS has a single ISO which allows you to select the DE.
- Manjaro does offline installs of all DEs. EOS offers an offline install of only XFCE. The other DEs are available through the online installer.
- The Manjaro forum is focused on distro support. The EOS forum encourages more community through off-topic exchanges.