If you are a mountain lover and wish to dive in valleys, go north for green and white mountains. For the beaches ofcourse and a lot of hospitality, South India. That's the beauty of India it's best in every zone from every direction. Hospitality of Rajasthani and Gujarati cultures in North and Ruins of historical wonders make it worth it to travel up. While the soothing sunsets and best of cuisine make South India a gem. About Travelling, according to my experience, travelling in South India is a bit more expensive than North. But it's safer. But yes, up in the mountains, the difficulties of travel increase if you are to explore offbeat places.
About Travelling in May, you won't find much snow in the North but the heat of South might be excruciating too. It will be better to explore central India with Green Mountains and Historical remains.
May is not a good month for travelling South because of peak summer. I suggest North India. North East is even better. Guwahati can be a good vacay spot.
North india is a better option, you can visit the unexplored places in himachal & uttarakhand.
Just to mention a few:
*Thachi valley - unexplored beautiful village
*Mukteshwar
* Auli
Its depends on your priorities, if you want to see chilly hill stations and trekking go for North india (Himachal, Uttarakhand, Kashmir) if you want to see beautiful beaches or temples go for south india. your question was regarding summer than yes except of Hill stations...plain area of North is very hot in May compare to south.
North india specially mountainswill be a better option in may , because it will be very hot in South India during the month of May , for visiting south India monsoon or post monsoon will be better, that is June to October period