I am asking as the area under the PV graph for the Isothermal
compression process is greater than the adiabatic compression process.
The problem with your figures is neither involves the same volume change. Since you are interested in comparing the work done by both process, and work is the integral $\int_1^2pdV$ between the initial and final volume, you should probably compare them for the same volume change starting with the same initial pressure. See Fig 1 below.
Fig 1 compares an isothermal compression to an adiabatic compression that begin at the same pressure for the same volume change. Note that the magnitude of the work (area under the curve) is greater for the adiabatic process than the isothermal process. But since the work is done on the system, the work is negative work.
Normally when we talk about more or less work being done we're generally referring to the work done by the system (expansion work), i.e., the magnitude of positive work. So in terms of the amount of work done by the system, more work is done for the isothermal compression in the sense that it is less negative (and therefore more positive) than the work done for the adiabatic compression.
Hope this helps.