Carol, the essence is in the rhythm, not in the word presentation, in this form, unusually, the layout does not play a part in the rhythm,( try reading both versions aloud into a tape) like for instance in the limerick, where there is a definate constraint of the rhythm in the line length, in Higgledy Piggledy IMHO it is treated as if it were 2 lines of equal length (and rhythm)of aa
the Horowitz one could be written
Higgledy Piggledy, Vladimir Horowitz Played the piano ,While picking his nose

Psychoanalysis,Failed to dissuade him,As quick or as well As the snot on his clothes.

whereas in the Limerick it is 5 lines of aa bb a eg
There was a young girl of Madras
who had the most beautiful ass
Not round and pink
as you probably think
it was grey ,had long ears and ate grass