Post-war histories make it clear that Alexander was personally brave, had an equable temperament and was a good leader of men but not a great technical general, and needed a good chief of staff to operate effectively. Montgomery on the other hand was a difficult personality (especially to his peers and those above him) but was a skilled technical general and had a great grip on what his subordinates were doing.
If Alexander was in charge he would probably have been less forceful in changing the COSSAC plan, and less clear on the critical objectives for the invasion plan, but would have probably have worked much closer with Eisenhower. Overall the Battle for Normandy would have taken longer, but would still have been successful.
Bombarding the beaches for 6 hours would have allowed the Germans to concentrate reserve units at the threatened sectors and bring up more ammunition for their artillery, leading to a worse slaughter at the beaches.