8,000 BTU vs. 10,000 BTU Portable A/C Unit - Will the 10,000 BTU unit cool the same room X degrees more if all other variables same the same?
Basically, a BTU is the amount of heat required to raise the temperature of one pound of water (at or near 39.2 degrees Fahrenheit) by one degree Fahrenheit 

So, an AC unit with the capacity of 10,000 BTU's per hour can cool more air (a bigger room) at the same rate, or the same amount of air faster than a unit with a capacity of 8,000 BTU's per hour.

So, in the exact same room under the exact same conditions, the larger AC can maintain a lower temperature than the smaller one.

If you have the AC set at 62°F and it never reaches that temperature and shuts off then the unit is overloaded and has to rest the compressor to keep from freezing up. Or it is possible the freezestat is shutting the compressor off when the evaporator coil freezes up. Either way, setting it to 62° is futile since it apparently cannot get to that temperature.

It appears your current unit can only get to 68° so that would be your maximum low set point for that unit.

A larger unit should be able to get to a lower temperature under the same conditions. But it still may never make it to 62°.

Good luck!