I personally don't think a few khz's one way or the other is going to make a major difference. In theory, it will, of course.
But we're not talking 50khz vs 12 khz, here, which would be a measurable difference. In this case, it is only 10 vs. 12 khz.
Keep in mind that jewelry gold is alloyed with copper. This alloying shifts the conductivity somewhat, rendering the whole higher freq / low conductivity debate a bit "fuzzy."
10K gold, for example, is well up in range of conductivity - I've found that 10K class rings are as close to screw caps as to anything else.
A few khz's here or there is the stuff forums thrive on, but which is mostly just grist for the prattle mill.
My vote is for 6 of one, half dozen of the other.
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As to the detector in question, I was hunting side by side with it until you got it - the guy you purchased from is my hunting partner.
Now I can say that the Sidewinder in question is going to give you options the Cutlass II won't. For starters, there is a SENS control and a push button for pinpoint... both of which the Cutlass lacks. At that point it is much like one of the various Silver's.
It also allows you to ground balance the detector to your locale as well as peaking the threshold, by "tweaking" internal pcb adjustment pots. By tuning it to fit your needs this way, you control the performance. Here, it's become more like a Bandido model.
The 8" coil on the unit, the classic Tesoro "Brownie," is one of the best all-round coils ever made, IMHO. Tesoro pioneered the printed circuit searchcoil and sealed pancake housing. These coils are both rugged and durable. Some of you may not remember, or even know, that Troy Galloway, of Troy Detectors, Inc., first hit the scene with Tesoros. The Sidewinder, as it happens, was one of his favorites.
Added to all this, is Tesoros untouchable service committment.
For the money you spent, I don't think you could get a better deal on a 'beep and dig' detector