Overnight in cordoba

Absolutely !!!

Same day Stop and go from my point of view.

Yes, you can see most of the Cordoba sights in a single day, then move on to Granada. I, however, recommend staying the night because this will allow you ample time to see the major sights, and also stroll around one of the most beautiful and most walkable cities in Spain. The patios throughout Cordoba are awesome and even private homes showcase them for the city's visitors pleasure. Do yourself a favor, spend the night in Cordoba, explore the city, see more than just the Mesquita. Granada will still be there when you arrive the next day...

Another vote to stay overnight. It's a lovely small city and less crowded at night.

I was happy to spend a night in Cordoba. The feel of the Jewish Quarter, around the Mesquita, is much nicer once the crowds thin out. We were driving and stayed at Hotel Hesperia Cordoba. If you aren't driving you might prefer something in the old center; for us the free parking and easy access of our hotel made it ideal. It's a short walk across the Roman bridge into the old quarter, so very convenient, and had a great view of the bridge and Mesquita from the roof (pool and bar area) in the evening.

If you stay overnight in Cordoba, how much time does that give you in Granada? I would ideally stay at least two night in Granada, so you have the option of a morning Alhambra reservation. The direct trains from Cordoba to Granada depart only at 11:00 and 19:00, so if you're not staying overnight in Cordoba, you might choose the 19:00 train; there are also direct bus options or more trains with a connection.