Ubuntu Budgie comes with tilix by default which may not be suitable for many. When I tried to replace it with xfce4-terminal, I found that nearly most answers included one of the two steps I mentioned below, i.e., editing dconf or updating alternatives. For me neither of them worked when done separately, but when I used them together I was able to change the terminal-emulator.
Steps:
Select /usr/bin/xfce4-terminal.wrapper as your default. there are two modes auto and manual.
gsettings set org.gnome.desktop.default-applications.terminal exec /usr/bin/xfce4-terminal
gsettings set org.gnome.desktop.default-applications.terminal exec-arg "-x"
And now you have xfce4-terminal as your default.
NOTE:
1. Replace "xfce4-terminal" by the one of your choice.
2. If you cannot see your terminal in step 2, use sudo update-alternatives --install <link> <name> <path> <priority>. More about it here.
3. gsettings is a dconf editor. More about it here.