I don't know if this is a little too late, but I might just add in a few thoughts...
Ionizing radiation (x-rays or gamma rays) will interact with matter through three basic processes: the photo-electric effect, Compton scattering, and pair/triplet production. In soft tissues, the photo-electric effect is dominant for the lower kilovoltage energies, and the Compton effect becomes dominant in the higher kV and megavoltage energies. But the net result it that photons interact and produce electrons that travel through the tissue.
As others have indicated the electrons will travel through cells and generate free radicals and reactive oxygen and nitrogen species. (They can also do direct damage by ionizing critical targets although I believe this is less common.) These then interact with critical targets generating damage.
One thing that's important to understand is that cells are experiencing this kinds of damage all the time. The process of respiration generates reactive oxygen species and these generate damage that your cells have to deal with. Background radiation also contributes to the damage, but from what I understand the background radiation damage is orders of magnitude less than that from other processes. So your cells exist in a steady state of damage and repair all the time.
The next question is what are the critical targets?
There is a lot of evidence to suggest that DNA is the most sensitive structure to this damage. For example you can incorporate Auger-emitting isotopes (they emit electrons with very short ranges) into various different organelles and the cells that have them incorporated into the DNA show the lowest survival and/or clonogenic capacity (the ability to form colonies). DNA is not the only sensitive structure. Mitochondria, for example, are also sensitive to radiation. And given high enough doses of radiation, even cell membranes will begin to break down. Cell "death" can have a number of different meanings. In terms of cancer control, often we're concerned about 'clonogenic death' - stopping the cell from reproducing. But on top of that you can have apotosis, which is a process where the cell detects enough damage that it triggers a set of processes whereby the cell commits suicide in a pre-programmed way. You can also have "necrotic" death, where apoptosis doesn't happen, but enough other processes shut down that he cell simply can't go on to do what it's meant to do - or example being starved on oxygen.
At different incident energies these patterns of energy deposition along the electron tracks will change and the density of ionizations can lead to differences in the effectiveness in the ability of the radiation to kill cells, but when comparing x-Rays with gamma rays the differences are generally small. Dose, or the amount of energy delivered per unit time, is most strongly correlated with effect. There are many other factors that can modify the effectiveness of the delivered dose. These include the amount of oxygen present, the phase of the cell cycle, the repair mechanisms in the cell, and other factors such as the influence of the local environment on the cells' ability to divide (repopulation).