First of all, the plain glass will protect your new stained glass panel from the elements. If you leave it in, you can avoid weatherproofing it, thus taking a substantial amount off your price. All panels that need to be weatherproof have to be made using leading technique. Leading does not allow as complicated of a design as Tiffany style, so you would also be limited in your design choices. However, even a leaded panel can be made very beautiful, so if you prefer to remove the plain glass - go for it.
But the second reason is that a stained glass panel, while weatherproof, is NOT insulated. So if you want to keep energy-saving properties of the plain glass, DO leave it in. It normally will have two glass panes with gas between them, making them more energy-efficient.
There are cases when home-owners want to remove the existing panes, because they might be textured clear glass, or there are plastic or wood mullions inside, between the two panes that would be visible through stained glass. If that is the case, it is a matter of taste and ingenuity.
In case of mullions being in the way, a stained glass piece can be created that works them into the the design. I have just created an entire doorway set - transom and sidelights that work with existing mullions and hide them from sight. I will go ahead and post a photo as soon as it is completely installed. Another option is, if you are handy, you can fairly easily remove one of the panes and take the plastic out and then put the glass pane back. You will, however, in this case release the gas inside that helps with heat-insulating properties. So although two panels of plain glass with just air between them will still insulate better than one, the window will lose some of its efficiency when using this method. Another problem with this method, is that you may end up trapping some condensation inside. Although it does not harm anything, it may be annoying to look at. The good news, you would only be able to see it on the outside.
Now if you have an existing glass panel that is textured glass, it is totally your call. You best bet is to hold your newly-made stained glass insert against it, and see if it spoils the desired effect. If you want to mitigate this issue from the get-go, your stained glass panel can be designed using textured glasses, whose appearance will not be affected too heavily by the refracted light from the outer textured panel. Such clear textured glass would mostly spoil the effect if you are using flatter types of glass in your panel, especially if the panel is sand-carved as well, or if there are painted pieces in it. But even then, the change may be insignificant, so you can just try holding up some colored glass against it to see if it makes enough of a difference to you to bother about it.
So there you have it. In my opinion, it is better to plan ahead for it and take your existing panel in consideration when designing your stained glass window than remove the existing one. It is important to note, that when installing a stained glass window, especially in a humid area, like a bathroom or, I do not know, like Florida :), it is best to leave some vents open. It is not rocket science. Trust me, you can do it. You can read in detail about window installation and vents here http://thelastunicornstudio.com/how-to-install-stained-glass.html.