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).
outdoors.stackexchange.com/users/3200/requiem
The main reason it's buried is to keep it from washing into water supplies.
The ground provides natural filtration, where surface waste is fully exposed to the elements and can flow along the surface until it reaches a stream or pond.
Yes, digging holes might be bad for one plant, but it's a whole lot better than polluting a water supply that animals (or even humans) might consume or people might swim in.
You could bag it and take it out with you if you really want to, but you aren't doing much harm if you dig appropriately sized holes.
Besides, plastic bags are worse for the environment than holes in the long run.
outdoors.stackexchange.com/users/3626/pheidlauf
If you were the only visitor to the area, the lowest impact would be to defecate on the surface and leave it.
Few animals bury their waste, so natural disposal has evolved around dealing with surface waste.
However, you aren't the only visitor.
Burial slows decomposition and disrupts the soil, but it reduces the ability of microorganisms to reach water supplies, and it keeps the area looking cleaner.
Packing out eliminates the impact to the local area, but increases the net impact because now you need to deal with whatever you packed the waste in.
Waste-disposal techniques are about reducing the collective impact of many people in an area, rather than the impact of the individual.
outdoors.stackexchange.com/users/3112/Mark
In some heavily used areas, especially where there's little chance for natural decomposition to occur (such as at high altitudes where there is poor soil), you're required to pack out all human waste.
For example, climbers on Mt. Rainier in Washington are required to carry specific bags to pack out their waste.
This is not the most desirable configuration for the climber, but is the most effective way to leave no human waste behind.
Other than packing it out, there's not much you can do besides bury it.
Burying the waste is preferable to leaving it exposed because buried waste is less likely to be carried into nearby water sources by rain runoff.
outdoors.stackexchange.com/users/208/nhinkle
It is not.
The lowest-impact solution is to use a poo-pot.
These are compulsory in alpine areas here in New Zealand.
Pack it out - Poo pots
outdoors.stackexchange.com/users/3079/Greenstone Walker
According to leave-no-trace principles, one should bury human waste (poo).  But burying damages plants and roots.  Is this really always better than not burying it and pooing on the surface?  (Of course, the only way to truly leave no trace is to not go at all.)  Edit:   This assuming a context when I am carrying everything on by back; solutions that require carrying significant additional mass are not preferred.
Is burying human waste always the lowest-impact solution?
outdoors.stackexchange.com
<leave-no-trace><human-waste>
outdoors.stackexchange.com/questions/6373
outdoors.stackexchange.com/users/566/gerrit
Waste-disposal techniques are about reducing the collective impact of many people in an area, rather than the impact of the individual. Burying the waste is preferable to leaving it exposed because buried waste is less likely to be carried into nearby water sources by rain runoff.  Burial slows decomposition and disrupts the soil, but it reduces the ability of microorganisms to reach water supplies, and it keeps the area looking cleaner.  In some heavily used areas, especially where there's little chance for natural decomposition to occur (such as at high altitudes where there is poor soil), you're required to pack out all human waste. The lowest-impact solution is to use a poo-pot.  Burial stops faeces entering water supplies, though waste should be packed in heavily used areas.
In heavily used areas, packing faeces is more appropriate. Burying waste stops it from going into water supplies.