Some interesting and good info posted above, but one thing that is missed here is not whether or not the piezo or preamp electronics are good or bad, but more important is how well they are matched to each other.
I've said countless times before, and it seems often forgotten, that impedance mismatch is the scientific reason why pickups can sound bad, whether passive or active (with a preamp).
Piezo elements, no matter who makes them have an impedance of at least 1M Ohms. That's 1 MILLION Ohms.
The preamp needs to be matched or calibrated with proper electronics on the INPUT to the preamp to accept the specific output impedance of a specific model of piezo element (which can vary widely +/- 15% even from the same manufacturer).
The cheaper pickup/preamp combos likely have little or zero calibration in them, and the difference in price to the higher end Fishman, LR Baggs and Mi-Si pickups, is likely due to the fact that they ARE calbrated, each to the individual piezo element sold in the box as part of the QC process.
I have spoken with design engineers from both LR Baggs and Mi-Si and can confirm this from first-hand conversations.
Many folks want to gloss over all the technical reasons and just play, and that is fine,
Maybe the reason that the Artec piezo rod pickups sound better with the cheaper preamps (like Belcat, whose web site gives a 404 for me now) is that they are a better electrical and impedance match to the cheaper preamp units than the dozen-for-$10 cheap Chinese piezo rod pickups that are typically the same thing sold as stock items when installed in most Kala, and other similar Asian-assembled ukes.
Budget varies widely amongst buyers, as does tolerance for learning the science behind how it works.
Some folks are easily satisfied with anything that makes a sound, but after working professionally as an audio engineer, I have experience enough to tell the difference between the low-cost vs high-cost units.
I will admit that I am normally a frugal person, but this is one case where for critical listening and better sound, you get what you pay for.
Since we do not all have the same goals, YMMV. It's all good to me, and I will not put down the choices other folks make, but please educate yourself as to why things sound the way they do before you spend the money.
You can read my previous encyclopedic explanations about pickups, mics, recording, and how to improve the sound of all of this via the FAQ link in my forum signature below.
The main thing, is use whatever you can afford and just keep making music if all of my tech talk gives you a migraine, I wont mind, and I am only trying to help by sharing my knowledge and experience here.
Shaka...