There are a few things to consider here before I can give you some more direct answers.

Firstly, Cairn is an exceptionally broad term, which encapsulates both simple interment of human remains within a loose pile of stones as well as more elaborate chambered tombs like Passage Graves and Long Barrows. Different burial monuments occur at different times and different places during the European Neolithic. Partly this is driven by the movements of people and ideas, and subsequent or immediate regionalisation. However an important factor is geology. In short, it is impractical to build a Long Barrow style burial cairn in Neolithic Sussex, for the simple fact that there is no suitable building stone. As such, during the period during which Cotswold-Severn Long Cairns are current, regions without good access to good building stone will often use timber and earth to build very similar monuments, that simply do not preserve the same way archaeologically.

Secondly, There are variations in burial practices within monument types, as well as between them. This may represent changes throughout a period in which a particular "class" of monument was in vogue, or simply be variations contemporary with one another. Further dating programs will be needed to bring greater resolution to this question by bringing large data sets to bear on the problem.

Now, down to brass tacks I'll be able to give a picture as painted by the archaeology of the Early Neolithic in Britain by using the well-studied Cotswold-Severn Long Barrow group as an example. Principally I chose this group because if the variety of practices there is evidene for, and the quality of archaeological work done here, and due to the generally favourable preservation. Only two, arguably three, Long Cairns of this type (with a fourth presently in the works) have been well excavated to a modern standard which allows for the careful examination of the interred human remains (Saville 1990; Benson & Whittle 2015; Britnell & Savory 1984). Others have been excavated, but frankly the work was not up to standard, or the sites where simply too heavily damaged.

Hazelton-North had two lateral passages and chambers, within which human bone was found preserved under layers of collapsed cairn material.

Both chambers were found to still contain human remains, much of which was disarticulated. The south chamber had 14 separate adults, roughly 6 to 11 pre-adults, and a foetus, deposited in two groups, one in the chamber and passage, the other in the entrance. Long bones seem to be under-represented, and skulls placed in groups against the walls. The north chamber had four adults, between fourand six pre-adults, and a foetus , the north entrance contained one complete extended adult male inhumation two more adults, and two sub-adults. Cremated bone was also found.

This evidence suggests that the people who built Hazelton North where in some cases interred and left to rot, in some cases put in as defleshed bones, cremated, in some cases it has been interpretted as likely some of the bones where taken out of the chambers, rearranged, and put back (Saville 1990; Darvill 2004). This degree of variety in burial practices is within one monument over a span of less than a century.

Similar findings where noted at Ascott-Under-Wychwood, and Gwernvale; and is implied by the reports of earlier excavations (Benson & Whittle 2015; Britnell & Savory 1984; Darvill 2004). The earth built barrows in Britain have very poor preservation, but the assumed and received wisdom is that the early neolithic was marked by a variety of burial practices. Most notably the interment of disarticulated remains, and the living returning to take bones away and rearrange them, possibly as part of an ancestor cult. The lack of gnawing by animals (there is some evidence, but not a lot) indicates corpses being pinched by carnivores is a minor component of the taphonomy.

Beneath some Barrows features have been identified and interpretted as "timber mortuary enclosures" a sort of charnel house, within which corpses would be left to decompose. Once the flesh had rotted away, the bones where presumably gathered, curated, and later interred.