I believe, and I stand to be corrected, that a generator that has field coils that rotate, generating coils that are stationary and rectifies it's output using diodes is known as an alternator. A generator that has stationary field coils, rotating generating coils and rectifies it's output by commutation is known as a generator - still with me?
I can't see any reason for similarly rated generators and alternators to have different current outputs at low rpm. Once an alternator/generator is producing current, the device is self sustaining ie it produces it's own field current without the need for a battery (although the battery is not needed to produce field current don't even think about removing it as it forms an integral part of the regulating circuit. If you take the battery away when the alternator is running you can literally blow things up).
However consider the following....
The problem with commutation, which was all you could do before diodes were invented, is that the brushes and commutator can arc and overheat easily. High current output requires a large mechanical design size which is why size for size alternators have a higher output that generators. The idea that generators have poor output at low rpms could stem from the fact that size restriction meant that generators were rated with very little, if any, headroom ie barely adequate rating at high rpm would result in below adequate rating at low rpm.
A type of generator that would certainly suffer at low rpms would be one incorporating permanent magnets rather that electro-magnets. The output of this generator can only be controlled by the speed of rotation. Any excess current has to be shunted to ground via a big resistor. This is inefficient and hot! In a situation that involved high rpms and low load requirement (fully charged battery and no auxiliary equipment switched on) the regulator would get very hot, so the generator would be rated with no headroom. At low rpms with high load requirement, the output of the generator would be insufficient and the battery would discharge. I believe it was quite common in the good old days for cars in a traffic jam in winter to discharge their batteries fairly quickly.
My had hurts now, I'm going to the pub for an Xmas drink....