We have both - drawers and shelves in wardrobe.

In baby's room we have nappies, socks, singlets, growsuits, wraps, cloth nappies etc. in drawers and proper clothes, blankets and just stuff on the shelves.

In DD's room we have all "small" clothes like singlets, socks, Pj's, hats etc. in drawers and other clothes on shelves.

You could prob do without shelves if you had to but as they grow older they will need more space for more and bigger clothes!