When comparing Eterm vs Termite, the Slant community recommends Termite for most people. In the question“What are the best Linux terminal emulators?” Termite is ranked 9th while Eterm is ranked 28th. The most important reason people chose Termite is:
Termite is a minimalistic terminal emulator. It does not need too many resources to run and it's designed primarily to work with window managers.
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Pros
Pro Requires very little memory
Eterm requires only around 9 MB of RAM per terminal instance.
Pro Transparency support
Eterm has pseudo-transparency support. This allows the user to make windows look less imposing (particularly in Terminal emulators which can comprise large chunks of text).

Pro Minimal terminal emulator
Termite is a minimalistic terminal emulator. It does not need too many resources to run and it's designed primarily to work with window managers.
Pro Vim-like behavior
Termite supports a command mode which is very useful if you prefer to use Vim-like keybindings. It takes inspiration from Vim, one of the most popular text editors, so someone who is used to Vim's commands will find themselves at home.
Pro Simple configuration
Termite is easy to configure. Reconfiguration does not require logging out or rebooting.
Pro Works great with a tiling window manager
Termite is most suited to a tiling window manager with a simple config file.
Pro 24-bit "True Color" support
Termite supports true color palettes, meaning that it allows for up to 16,777,216 possible colors.
Cons
Con Focuses too much on looking pretty
Eterm focuses a lot on being customizable and looking good, instead of focusing on features or power.
Con Cannot set specific parameters through CLI arguments
Setting specific parameters through CLI arguments is not supported in Termite.
Con Problem correctly displaying images while using compton
Images can sometimes not be displayed correctly in software such as ranger while using compton.
Con Difficult to install in some distros
Con Slow text rendering
Con Limited documentation
There's only short manpages and a README on the front page of the repository which has few details on additional configuration and features.