I'm currently a fan of acrylic, especially with a heavy weight/clamp. I initially got the combo (which I linked) because a number of the older special edition LP I own are warped (clear/tinted stuff from the 70s did not hold up). It helped flatten them out enough so that playback didn't have any noticeable warping noises. After using it with a bunch of good vinyl, I found it did help tighten the bass response a bit while bolstering the mids a smidge. Both of which didn't make too much of an overall impact for my setup because the gear I'm running is fairly warm and vibrant for mid-fi (Denon VL12 Prime turntable, Teac AX-501 and Nobsound 6P1 amps, Yaqin MS-23B Phono preamp, Yaqin CD3 line buffer, and Pioneer FS52 and BS22 speakers with SP-8 subwoofer), and were only easily noticed when using the monitor out with my HD6xx and T1.2 cans.
I did not (and still don't) like cloth mats. They have a bad habit of generating and holding static electricity. Plus they leave detritus on the bottom side of the LP. I did find that putting the cloth mat between the turntable platter and the acrylic mat helped isolate some of the vibrations generated by the floor-standing speakers and subwoofer, but that is more anecdotal than anything else.
Edit: Also, a handy benefit of the acrylic platter is being able to easily and accurately set the anti-skate controls on turntables that have 'em. Without risk of damaging the stylus or vinyl, even. Start the table without any vinyl, place the stylus about 1/4 the way to the edge of the acrylic, and adjust the anti-skate control until the tonearm doesn't move in either direction. Too much or too little will have the tonearm either heading towards the center or outside of the platter.