The question uses the term "Usually" which is not a correct description , however the decay schemes can be understood by analzing the process in detail.
An alpha particle is identical to a helium nucleus, being made up of two protons and two neutrons bound together.
There are models in which a nucleus can be seen as cluster of alpha-particles; say Carbon -12 as composed of three alpha particles.
In the decay process it comes out from the nucleus of its parent atom, (invariably one of the heaviest elements) by quantum mechanical process of tunneling and is repelled further from it by electric force , as both the alpha particle and the nucleus are positively charged.
The process changes the original atom (its mass number decreasing by 4 and atomic number by 2) from which the alpha particle is emitted into a different element called daughter nucleus.
Sometimes one of these daughter nuclides will also be radioactive, usually decaying further by one of the other processes.
This tunneling through the barrier depends on the barrier potential defined by strong nuclear interaction and as the decay process is intended for stabilizing the nucleus to lowermost energy levels therefore many a time the daughter nucleus is found in the ground state but this energy transfer also leads to
daughter being in an excited state and later reaching the ground state by emitting a beta particle or a gamma radiation.
Beta electron emission occurs by the transformation of one of the nucleus’s neutrons into a proton, an electron and an antineutrino.
Beta positron decays is a similar process, but involves a proton changing into a neutron, a positron and a neutrino.
The above process gets into motion for unbalanced nucleus where excess proton or neutron is found.
The decay process is guided by weak interaction and the parity and angular momentum conservation/non-conservation are guiding principles which determine the transition to be allowed or forbidden.
The Q value of such reactions plays an important role and the presence of a free proton after its conversion and its spin relations with the associated electron plays a significant role as to the decay leading to a Fermi-transition or GT-allowed or a mixture of the two.
The beta decay process usually lands a daughter nucleus in an excited state from where it goes to ground or lower energy state by gamma transition.
The detail analysis of the transition is essential to find the final energy of the daughter nucleus.
One can attribute it to the complexity of the beta decay process.
After a nucleus undergoes alpha or beta decay, it is often left in an excited state with excess energy and goes to stabilizing itself by gamma emission.
For a detailed analysis one can see:
Chapter 8 Beta Decay (pdf) from a Nuclear Chemistry course by Loveland.
Gamma radiation is used when the radiation source is outside the body and we need to focus it into a tumor that's inside it. For these situations, if we used alpha radiation, it would just get stopped at the skin, which is definitely not a good thing.
This type of external-beam therapy can also be done with charged particles, known as particle therapy, in which case you have the advantage that the sources can be more consistent and that you have better control over the focusing (since you can use electrostatic lenses and magnetic fields to shape the beam). However, once you're in that arena, proton therapy is likely to have every advantage of helium-ion beams, and it will be much easier to produce.
Alpha emitters are good in situations where you can get them right next to the tumor cells you want to kill, which probably means that you're including the alpha emitter in some biochemically-active molecule (a radiopharmaceutical) that gets preferentially concentrated in the tumor.
This does seem to be used in practice, though it seems that most therapies of this type use beta emitters, which have a slightly larger radius of action.
Best Answer
Radiometric dating tends to use a nucleus that changes into some other easily distinguishable nucleus. For example uranium decays to lead 206 and 207, which can be easily measured in a mass spectrometer. We measure both the uranium concentration and the lead concentration and infer the age from how much of the uranium has changed into lead.
The problem with gamma radiation is it doesn't produce a chemically distinguishable product. Gamma decay is effectively a decay of the excited state of a nucleus to a lower energy state of the same nucleus. So there is no way to tell how much of the original parent nucleide has decayed.
By contrast alpha decay produces a daughter atom with an atomic number lower than the parent by two, and beta decay produces a daughter atom with an atomic number higher than the parent by one. In both cases a mass spectrometer can easily tell the difference between the original atom and the product.