Why the difference?

Others may disagree, but I think the drive system is a non-issue as long as it is well implemented. At a practical level a turntable's suspension and the surface you place it on has more impact on the sound.

The most likely explanation is that the TT mayby spinning a little fast. Rega is known for this. I would try a speed control device. If you call The Cable Company, they should be able to send you one so you can try it in your system before you commit to buying.

"Drive", "Pace, Rhythm and Timing" etc are all ways of describing pitch accuracy. A properly executed drive system will keep up with the demands of stylus-in-groove. As long as the main bearing is also well executed, and there is a successful treatment and reduction of air-borne and floor-borne resonances, then all should be well.
The rest of the sound will be taken care of by arm and cartridge choice, and it can be here that things get interesting...synergistic combinations are what to aim for.
Unfortunately, our industry can be plagued by pseudo-science and the mystification of terminology - all good for advertising, but often enough to make 'reading between the lines' absolutely essential if you are to keep a clear head.
Just the opinion of a fellow-traveler. Enjoy the music!

One factor to consider is the effect of the motor vibrations. Remember that the cartridge is taking tiny miniscule vibrations and amplifying those. If the motor is directly coupled to the platter, you have to then deal with a greater possibility of that motor imparting vibrations to the platter and then to the stylus. It's one of the claimed advantages to belt drive TT's as the separation between belt platter and motor helps to isolate these vibrations.

Seikosha gave a good answer. Any influence to the diamond will give a result you can hear. Normally there is a shift of the reproduced frequencies (more bass, smooth highs...) and some like that and write what "sound" their turntable has. A good turntable has no sound. It is a neutral medium, the better it is, the more information you will get from your records, no matter what music is played. Analog is a mechanical reproduction, it is based on science, material knowledge and precision. When done right, it can't be cheap. Unfortunately you have no guarantee that you will get a top product for your money because all Designers are perfect :-)
This creates of course some frustration and that is the reason for some to look for yesteryear designs in the hope they will get a serious product for small money. Sometimes it works but most is not worth to talk about.
Rim / Idler drive was a technology when nothing else was available and the only advantage was the acceleration from scratch (important for Radio Stations who were not interested in a wide frequency area we want to have from High End units). All those rumbling devices were replaced as soon as possible with Direct Drives when they became available. they can hold the speed for they have always corrections while spinning (in a good System you can hear it easily when you know what is going on). High End is running in circles, a few years one Design is hip, after some years that Design will follow and so on. And behind everything is the need to make money. So it is normal that you will find more and more refurbished items which were bought for $250,-- and after some wood work and replacing a few parts it is offered for $10k.
It works. But Physics is Physics. Normally you can't change it. The only exception is High End.