As far as tone is concerned, much can be done to the sound of a theremin through processing. As Bob Moog said in ELECTRONIC ODYESSEY, "...the theremin is completely at home in the electronic environment". If you don't like the sound of your theremin, experiment with ways to change it into a sound you do like.
If you are a violinist and you don't like the sound of your fiddle, you have no choice but to get rid of it and buy another instrument. As electronic musicians, we have alternatives not available to acoustic players. I am often amazed by thereminists who say they don't like the sound of some particular theremin when so much can be done to change it. They shop for theremins the way they might shop for a clarinet or a cello!
The addition of a high quality EQ unit can do wonders for a theremin that lacks presence, or sounds thin and brassy, or too "throaty", or whatever. The problem is that the kinds of devices that will give you the results you're looking for can cost more than your theremin - especially if your theremin is an entry level instrument.
If you like the warmth of the tone produced by tubes rather than transistors, a unit like the TLAudio 5051 (http://www.tlaudio.co.uk/docs/products/5051.shtml) can radically improve the timbre of your theremin - even if the theremin you are playing is essentially a toy. You can pick a 5051 up on ebay for about $500.00.
I understand that's a lot of money for many people, particularly for newcomers to the instrument, but if you are playing at a professional level, and presenting yourself as a "thereminist" on national TV, you owe it to yourself (not to mention to your audience) to be the very best you can be.
As thereminists, if we really want to seduce an audience, we have to outshine the novelty of the instrument we are playing with the beauty of the music we are making.
Dats a biggy!