Beyond Compare 4.1 and newer require matching package and OS architecture (amd64.deb or i386.deb). Beyond Compare 3 - 4.0.7 require the i386.deb package on all supported versions of Debian and Ubuntu (32-bit and 64-bit).

Beyond Compare 3 on Debian 7, 8 64-bit
Enable 32-bit architecture support:

sudo
 
 dpkg --add-architecture i386

Graphical Install
Double click on the .deb package to install using the graphical package manager.

Terminal Install

sudo apt-get update
sudo apt-get install gdebi
sudo gdebi bcompare-4.1.6.21095_amd64.deb

Terminal Uninstall

sudo apt-get remove bcompare