With Firefox around , the current version of Epiphany doesn’t have any chance since there are using the same gecko engine and clearly, Firefox is better. However, the next version of Epiphany is attracting some developers since it will be using the WebKit engine by default
If you would like to get your hands on the Webkit powered version of Epiphany, you need to actually have the Webkit engine installed first then install Epiphany. And that involves a lot of dependencies headache. But, luckily, I found two ways of running Epiphany/Webkit: the Soft way from Michele Costantino and the Hard way 
. If you just want that thing running immediately , just go for the soft way but if you’re like me and you want a little bit of challenge, well, you know which one to pick.
Soft Way
Add the following two repositories to your /etc/apt/sources.list:
deb http://ppa.launchpad.net/stemp/ubuntu hardy main #WebKit & Midori
deb http://ppa.launchpad.net/michelinux/ubuntu hardy main #Epiphany-WebKit
Then reload your sources
sudo apt-get update
Now Install epiphany/webkit
sudo apt-get install epiphany-webkit
To run epiphany/webkit
epiphany-webkit
Hard Way
Install WebKit/GTK+
Download a nightly tarball source (small download)
You can head over and start installing but it generate a lot of dependencies errors if you don’t the right packages installed. To help you a little bit in your adventure based on my adventure, make sure you have the following installed:
sudo apt-get install libtool bison flex gperf libicu-dev libglib2.0-dev libgstreamer-plugins-base0.10-dev libgstreamer0.10-dev libxslt-dev libcurl4-openssl-dev libsqlite3-dev libjpeg62-dev libpng12-dev libcairo2-dev libpango1.0-dev libgtk2.0-dev gstreamer-0.10 gstreamer-base-0.10 gstreamer-plugins-base-0.10 gnome-vfs-2.0 libgstreamer0.10-dev libgstreamer-plugins-base0.10-dev gstreamer0.10-gnomevfs libxt-dev
Extract the tarball and from the resulted folder, Run the following commands to configure and build WebKit (choosing an appropriate prefix):
sudo ./autogen.sh --prefix=/usr/local
sudo make
sudo make install
Install Epiphany/Webkit
Make sure you have the following installed:
sudo apt-get install libstartup-notification0-dev libgnome-desktop-dev libdbus-glib-1-dev libwebkitgtk-dev
-Download the source tarball from here, extract it and from the resulted folder
sudo ./configure –with-engine=webkit
sudo make
sudo make install
To run epiphany/webkit
epiphany
