Very often, the "modified sine wave" is more like a square wave. The problem lies in the fact that a sinewave has a peak voltage that is sqrt(2) higher than the RMS value. For a square wave, the peak value and the RMS value are the same. And a "modified sine" is somewhere in between.
A normal battery charger works with peak voltage a little higher than battery charge voltage - a 12 V battery usually gets charged with around 14 V peak and a reactor (or the impedance of the transformer) takes care of the necessary current limiting. So the battery is only charging the few milliseconds when the voltage is higher than the battery back EMF.
Combining these two facts explains why you do not get a good charging from a modified sine wave. The peak voltage simply is too low. You can see this if you hook up an oscilloscope to the battery. Charging from a sine will give you little "humps" when the battery is actually charging. Use a current clamp (DC!) to watch the charging - you will understand what's going on when you see the difference between charging with sinewave and "modified sine".