Oishinbo

Each of these is a gourmet anime juggernaut, although from different generations. If you watch Food Wars for the cooking and not for the clothes flying off, check out Oishinbo, one of the big 3 that launched the genre. 

Both are about interpersonal relationships and food. Obviously Ryoutei no Aji is selling miso soup, but Oishinbo is promoting Japanese cooking more generally. 

Oishinbo is the OG of the cooking food anime. If you like a slower paced "rivalry" Oishinbo is for you.  

Both Cooking Papa and Oishinbo are gourmet anime based on manga from the mid-80s. Oishinbo originated the food critic trope (ie a focus on obscure knowledge about ingredients or techniques), but Cooking Papa pioneered the slice of life with cooking recipe included at the end. While it seemed like Oishinbo had the bigger influence on the gourmet genre for about two decades, after the mangaka got into political trouble over how he depicted the Fukushima Disaster, there have been a boom of more Cooking Papa influenced style manga and anime- with the signature focus on attainable and cookable dishes. So if you want to experience another OG gourmet anime, check it out. read more 

From the second generation of gourmet manga (mid 80s), these anime give an idea about the usual tropes. Ippon Bouchou Mantarou hews more closely to the first generation with a wandering chef pursuing the perfection of his craft, whereas Oishinbo is known for making the shift from the focus on the craftsman to the focus on the critic evaluates food. Of course this is no surprise as Big Joe is the author of both the Ippon Bouchou Mantarou manga and the OG gourmet manga, Houchounin Ajihei. 

Mister Ajikko is the third of the Big 3 80's manga that launched the gourmet manga genre. It is unrepentantly shonen, with all the 80's trappings. Rivals? Check. Skateboard? Check. Stereotypically girly female sidekick? Check. As an adult, it's a bit hard to watch more than one episode at a time, but hey, this is the manga that inspired Iron Chef. If you want something slower paced, seinen, but still with a food rivalry component, check out Oishinbo.