In more temperate climates (forests, jungles, etc.) burying feces is preferred as it will be broken up by microbes in the soil while being somewhat protected from the environment. Plant growth in these areas is also rapid enough that cut roots are generally a non-issue. (I'm assuming you aren't hacking through larger roots.) In general the warmer the climate the better the decomposition.
Deserts, canyons, and alpine areas above treeline represent special cases; there is generally a lack of organic soil in which to bury waste and vegetation grows very slowly, if at all. In such areas, particularly heavily impacted ones, packing out waste via WAG bags is preferred and sometimes legally mandated.
On rarely-visited routes in the high alpine there are two other options which are sometimes used: the first method is to go on a rock then toss it down a moraine or crevasse. The second is to smear it into a paper-thin layer on a rock facing the sun; the sun and wind will slowly bake and abrade it away. (It's worth noting that the Leave No Trace Center for Outdoor Ethics found most people don't spread it thin enough.)
Regarding toilet paper, many advocate packing it out. I've heard differing opinions on how well it decomposes in the wild, and often that's climate dependent. Outside of areas with good organic soil I would pack it out. Another option that many use is to skip toilet paper and use snow, rocks, or leaves instead.
In terms of supporting data, one Tasmanian study looked at decay rates of different products (facial tissue, tampons, as well as bleached and unbleached toilet paper) at different sites and with or without added nutrients (i.e. poo). The actual paper appears to be paywalled, but the results suggest unbleached paper is slightly better, tampons decay much slower than the other products (and should probably be carried out), and outside of alpine/subalpine areas decay proceeds at a good pace, particularly when combined with waste:
There was a significant site×time×treatment interaction in the generalised linear model for mean decay rates which included 6 m (a/w), 12 and 24 months (Table 2). At 6 months over autumn and winter mean decay of products was well-advanced at the coastal eucalypt forest and the grassy eucalypt forest, but negligible in the lowland rainforest, the heathy eucalypt forest, the montane moorland and the western alpine sites (Fig. 2). By 24 m decay was almost complete (at least 75% decayed) at all sites except the montane moorland and the western alpine site (Fig. 2). At all sites, except lowland rainforest, there was a significant positive impact of nutrient addition on decay (Fig. 2). The impact of nutrient addition on decay was most marked at six months over autumn–winter (Fig. 2).