That is true, in principle.
A bit slower is usually at least a bit better. The same principle that differentiates olive oil grades can be applied to juices.
A proper (albeit quite small) study on this seems to confirm this.
Quality Changes of Fresh Vegetable and Fruit Juice by Various Juicers KSBB Journal, Volume 29, Issue 3, 2014, pp.145-154, Korean Society for Biotechnology and Bioengineering
Concerning the juicers used in this study, slow juicer could be recommended to prepare the fresh juice in terms of the juice quality.
The slower juicers as well as the slower settings for multi speed devices increased the yield of the product compared with higher speeds. The assayed activity of the extracted enzymes, polyphenols etc was uniformly higher as well. But aside the small study design these differences were not earth shattering.
Fig. 4. Nitrate (NO) radical scavenging activity of grape juice by high- and low-speed juicer.
(Disclaimer: parts of my interpretation relys on very limited knowledge of Korean and the aid of machine translation.)
Luckily, the same team also published in English:
Antioxidant activities of fresh grape juices prepared using various household processing methods (Food Sci Biotechnol (2017) 26(4):861–869)
The grape juices were prepared using a low-speed masticating (LSM) juicer, a high-speed centrifugal (HSC) juicer, and a blender (BLD). The total polyphenol, total flavonoid, total monomeric anthocyanin, and vitamin C contents were highest in the LSM grape juice, and decreased in the order: LSM > BLD > HSC > GF. The antioxidant activities such as DPPH radical scavenging activity, and SOD-like activity were significantly higher in the LSM juice than in other juices and grape flesh. The antioxidant activities and the quality of grape juices were significantly affected by the household juicing method used, and an LSM juicer is strongly recommended for making healthy grape juice, rich in antioxidants.
The antioxidant contents of grape juices and grape flesh. (A) Total polyphenol, (B) total flavonoid, (C) total monomeric anthocyanin, and (D) vitamin C. Grape juices were prepared using a low-speed masticating juicer (LSM), a high-speed masticating juicer (HSC), and a blender (BLD). Grape flesh (GF) was prepared by removing seeds and skins from whole grapes. TAE tannic acid equivalents; QE quercetin equivalents; and CE cyanidine-3-glucoside equivalents. The results are expressed as mean ± SD (n = 3). Different superscripts signify significant differences (p \ 0.05) by Duncan’s multiple range test. ND not detected
Our research demonstrated that the antioxidant activities, and the quality of grape juices, were significantly affected by the household juicing method used. Antioxidant activities and nutritional properties of LSM grape juice were the highest, compared to those of other grape juices. Also, the consumption of whole grape juice is more beneficial to health than that of grape flesh because we can take more antioxidants from grape skins and seeds in whole grape juice. Therefore, an LSM juicer is strongly recommended for making healthy grape juice rich in antioxidants.
Same team, same methods, same limitations and problems. Since an undisclosed conflict of interest might be involved in endorsing so clearly commercial products (even as whole classes): These findings should be taken with a grain of salt regarding the health benefits.
Interpreting the results from these diagrams also has to account for different yields from the same source materials. While the concentration might be higher in a given glass, the efficiency of extraction and the total amount of deemed beneficial constituents from the sources is not to be equated with "juicers are better than the fruits and vegs themselves."
If, however, another, more subjective criterion would be permitted to judge the quality, just trust your nose and tongue. The taste of slower and more carefully prepared juices is usually more enjoyable.