The short answer
Both, for different meals. The medina is where Moroccan food lives: street stalls, Mechoui Alley, riad restaurants and rooftops over the Koutoubia. Gueliz, the new town, is where you go for French bakeries, international menus, long-running cafés and a glass of wine with dinner. Many visitors eat lunch in one and dinner in the other.
In more detail
In the medina, eat Moroccan. Around Jemaa el-Fnaa and the spice square you find the night stalls, the pit-roasted lamb of Mechoui Alley, sweet shops on Souk Semmarine and rooftop cafés. Mouassine, west of the souks, is where riad restaurants cluster along Rue Dar el Bacha: courtyard dinners, quiet tea rooms and plant-based cafés. Riad Zitoun, south of the square, has simple cafés such as Cafe Chez Zaza and Bakchich Cafe.
Gueliz runs on a different clock. Cafe Les Negociants has served coffee on Avenue Mohammed V since 1936. Amoud has made pastries, chocolates and ice cream there since 1982. You also find French bistros, Lebanese and Indian kitchens, sushi, artisan patisseries and organic cafés such as Ayaso Gueliz. Alcohol is easier to find here and in Hivernage next door.
The practical difference is access. A car or taxi can pull up outside most Gueliz restaurants. In the medina, many riad restaurants sit down lanes too narrow for cars, so expect a short walk from the nearest gate, and ask the restaurant how to find the door.
If you stay in a medina riad, your hosts are the best guide to the lane next door. If you stay in Gueliz or Hivernage, keep one evening for Jemaa el-Fnaa and a medina rooftop.