The short answer
Erg Chebbi, at Merzouga, is the easier and taller one: dunes up to around 150 m, a paved road to the sand and many camps. Erg Chigaga, beyond M'Hamid, is longer, emptier and harder to reach, with dunes up to about 100 m, a 4x4 piste at the end, few camps and no phone signal. Chebbi for a first trip; Chigaga for solitude.
In more detail
Erg Chebbi is a concentrated wall of orange dunes, about 22 km long, rising straight out of a flat stone plain beside Merzouga village. Its size and colour are why it fills the photographs. The other side of that is company: camps line the edge, quads and camel strings work every day, and in season you will not be alone on the crests at sunset.
Erg Chigaga lies far to the south-west, where the Draa valley ends. Our destination notes describe a dune field about 40 km long with crests around 100 m, no tarmac and only a scatter of camps. You reach it by 4x4 across open hammada from M'Hamid, and once there the camps are deliberately off-grid. Skies are among the darkest in Morocco.
The routes differ too. Merzouga comes with the Dadès and Todra gorges. Chigaga comes with the long palm corridor of the Draa valley and Zagora. Many travellers who come back to Morocco do Chebbi first and Chigaga on a second trip, and a long loop can include both.