Welcome, Londonforces!
If I understand the question properly, the main difference would be that the "standard" enthalpy of formation, combustion etc. refer to the reactant and products in their standard state. That is, at 298K, 1atm, and the corresponding aggregation state, in the most common allotropic form.
Bond energies usually don't specify the aggregation state at all - it could be a gas most often.
So a sensible use of the bond energies would need to correct the heats of formation by the evaporation and melting heats as needed. This is a very serious difficulty because these heats are often unknown but important. It's the same difficulty as when using a software to predict heats of formation, which gives an (inaccurate) estimate for gases at zero kelvin while we need liquids or solids at 298K.
Beware also, specifically for heats of combustion, that the produced water can be liquid or vapour. This corresponds to the upper and lower calorific value of fuels. Which one to use depends on the devices you have: recent boilers condense the fumes' vapour to extract more heat from the fuel.
----------
The other difficulty is that bond energies aren't accurate enough for many uses. As you accumulate errors over tens of bonds, the end result is inaccurate.
This is made worse because a reaction (for instance combustion) enthalpy is a difference between two big values: the summed bond energies at the products minus at the reactants. By using instead enthalpies of formation, you avoid this difference of big and inaccurate quantities, since the enthalpies of formation refer to the elements in their standard state, where molecules are already formed. They are also nearer to the measurement process and the normal use, where reactants are molecules, not separated atoms.
One more difficulty is when you have small rings or even cage molecules. You may apply corrections known for some small rings to the bond energy, with more or less success, but not for cage molecules, since these are too varied to fit in tables.
----------
So bond energies fail too often and by too much to be the general method to predict enthalpies of formation nor reaction. They are almost as bad as software for this task. But they are useful to
- Predict whether a reaction may occur.
- Predict at which atom a reaction will occur.
- Compute enthalpies of formation for molecules that resemble an other one that is tabulated, hence needs few corrections.