Which is better for a keralite, EE at IIT Mandi or engineering design at IIT Madras?

For obvious reasons, ED in IIT Madras is better than EE from IIT Mandi.

Since, you are a Keralite, you need to travel across the entire length of India whenever you need to travel back and forth from your home. Moreover, the climate will also be a minus factor. In case of Chennai, you can travel overnight and reach your home. The people there will be more familiar to you as compared to those in Mandi.

Engineering Design - 

• It is an amalgamation of all the engineering disciplines in a crude sense which can be easily seen by their curriculum. 
• The curriculum includes doing coding, mechanical labs and civil engineering courses, it even includes Electrical Engineering. 
• BTech in Electrical Design is a 5 year Program as it includes a compulsory six month internship (an entire semester) in the final year and a project in the final year of the course. Whereas, the courses at other branches last for only 8 weeks.

To summarize, IIT Madras offers you everything that IIT Mandi has and a lot more than that.

Mandi is situated in Himachal Pradesh, it has a very pleasing scenery. But keeping in mind the distance, weather conditions and the ease of living for a Keralite, Chennai is a much better option.