An arc gives a greater electrical capacity and a closer elcromagnetic field, so that you need less movement in order to control volume. With lesser movement there is also less risk to disturb the pitch field.
Since one wants a extended pitch field to allow accurate playing over 5 or more octaves, an antenna in stick form is better because of its lesser capacity and the resulting bigger electromagnetic field.
If you have further technical theremin-related questions, you may send me an email on frenkel(dot)thierry(at)orange(dot)fr
I’d prefer if you write in German , since my English is very bad and I’ll be able to give better explanations in French or German.