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.