Usually, the beta diversity is correated with read abundance (but if you use presence/absence data, it will be different). Probably the denoised reads have low abundance. And thus, it has less effect on the beta-diversity.

Maybe have a look at this paper:

http://nar.oxfordjournals.org/content/early/2010/06/14/nar.gkq545.full

You can also find some application of the MultiCoLA tool to datasets with or without noise removal. What we found - but this should be repeated for each dataset - is that generally rare members, including noise, do not have much effect on beta diversity patterns. The latter are mostly driven by the most abundant types. 

Thanks Jung and Ramette for your  teaching, I'll learn the paper. 

While I am not closely familiar with the paper posted by Dr Ramette (which is really interesting, btw), I would like to raise two points:

(i) Although I do not have data to support this, I believe that different widely applied measures of community similarity will be differentially robust to whether you denoise your data or not. Incidence-based indices, such as e.g. the Jaccard, but also unweighted UniFrac, can be expected to be sensitive to "noisy" data, or generally to the tail of "rare" taxa observed (i.e., OTUs or taxa represented by only one or two sequences). This would also be true for several more involved indices, like e.g. Chao's abundance-corrected Jaccard and Sørensen indices (where "rare" taxa are used to estimate "unseen" taxa). At the same time, abundance-based indices such as Bray-Curtis or weighted UniFrac would be more robust. In other words: what metric for beta-diversity are you referring to?

(ii) That being said, do you have a good reason to *not* denoise your data? I believe that if you conduct any analyses beyond PCoA plots on weighted UniFrac or Bray-Curtis distances, denoising will in any case be useful / desirable / necessary.

Thanks Thomas for your recommendations, I think I had to learn more about the denoising!