Why alpha decay usually leads to ground state while beta decay usually leads to excited state? When alpha decay happens the daughter nucleus is usually in ground state.
When beta decay happens the daughter nucleus is usually in excited state which is then de-excited by emitting gamma photon.
Why is this?
 A: 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.
