When there is an existing noun (as memorization) could we use the ing to form another one (memorizing)?
If so, what would be the difference between the two concurrent nouns?
Basically, yes. You can either use memorization or memorising as a noun. However, when there already exists a noun that carries the meaning you wish to infer I would recommend you use it:
Native speakers often use memorizing as a noun:
Understanding how these chemical processes work involves far more than memorizing. Memorization is required, to be sure, but memorizing alone doesn't lead to understanding.
Memorize is a verb, as in "He memorized his address."
Memorization a noun describing the process of committing something to memory.
Memorizing is already in use as a gerund or present participle of "to memorize." As in, "She is memorizing the lecture notes." Memorizing isn't used as a noun.