33Nicolas You don't need to start from scratch. You can run them either in parallel or you can install Budgie and remove MATE afterwards.
sudo eopkg install -c desktop.budgie installs Budgie
To install GNOME stuff that's included in Budgie ISO (Nautilus and terminal, for example) you need to run
sudo eopkg it baobab eog evince file-roller gedit gnome-calculator gnome-calendar gnome-control-center gnome-disk-utility gnome-keyring gnome-photos gnome-screenshot gnome-settings-daemon gnome-system-monitor gnome-terminal gnome-themes-standard gnome-user-docs nautilus nautilus-python onboard orca seahorse thunderbird yelp
To remove MATE, you can run sudo eopkg rm -c desktop.mate