You will need to run AWG #4.
Need to know what the load amperage is on the 100 amp panel. If interested, open discuss question page.
AWG # 4
AWG #8 copper will work but I personally would use #6 for that long of a run.
For that distance I would run AWG # 3 copper and install a sub-panel.
Normally you would use AWG #6 but for this long run and voltage drop I would recommend you use AWG # 4.
Depends on the size of the sub-panel in that garage. If you are installing a 60 amp sub-panel 400 feet away from the main service panel then use AWG # 4.
To answer this question a voltage has to be stated.
This is a voltage drop question. The voltage has to be stated before an answer can be given.
A 125 amp panel or subpanel requires # 2 gauge feeders and neutral. (# 2 awg is rated for 130A) However, depending on the existing load in your main 150A panel you likely don't have enough power to operate a 125 Amp subpanel.