We have been using spagnum peat for treating wastewater with great success (we call it the SOG filter http://hwt.co.za/sog-trickling-filter/). I have noticed that potable water applications are not very fruitful. What is the application you have in mind?
Both are very good adsorbent of heavy metals and organic pollutants. Lot of the research is carried out over the adsorbing property of the vegetable origin material.
The findings are to be confirmed by experiments in laboratory with the specific effluent for pollutant removal.
Are you looking at water treatment for potable use or waste water treatment / stripping specific elements out of water?
A few years ago I was involved in a project where we were stripping metals (cadmium and zinc) from groundwater using a peat sorption bed followed by a reed bed, we achieved a 99%+ removal rate and it took about three years for the bed to get loaded and need replacement (we had the water percolate through the peat bed that was about 5m long).
There are lots of references on the use of this kind of approach for groundwater remediation, so if you are after performance characteristics I would start there.