hey... you have posed a question that I had 4 yrs ago and questioned myself again few months ago.
it really depends on what you really want to do and how far your gf will go with this interest. Do bear in mind that assuming all of the specs between 350D & 20D, 3 things will certainly be different. i) handling feel, ii) AF system, iii) button layout interface
Companies like Canon does not make 2 cameras with same specs and charge different price. Obviously there's a difference and it is what I mentioned above. If your gf plans to just make this a fun and adventurous but no more than getting a little more serious, 350D is really a choice. However, if she does show interest and may float it into doing a little more serious-to-amateur-pro, I will highly recommend a 20D. But then, due to the shutter actuation cycles for both of these cameras to be around 50,000 cycles, I would suggest that you get a 30D instead of 20D, which the former has 100,000 cycles.
I kind of regretted getting 350D because it limits my creativity and ability when I tried to push beyond what the camera can do for me. But now the 350D is my good 2nd camera for my photo projects... still the regret is minimal because 350D is a good camera. It all goes back to whether to pay a little more or save a little more.
Good luck!