HaridwarHaridwar is one of the seven holiest places in India. (The others are Varanasi/Kashi, Kanchipuram, Ayodhya, Ujjain, Mathura, and Dwarka). What's so special about these places? Visiting them is believed to provide release from the endless cycle of birth and death. Thus, pilgrims attain "moksha" or liberation.
Understandably, this makes Haridwar very popular with Hindus who come to bathe in the holy water of the Ganges River, cleanse their sins, and visit temples. The Mansa Devi temple, which sits high on a hill in Haridwar, attracts hoards of pilgrims as the Goddess is believed to grant the wishes of those who visit her. The Ganga Aarti at Hari-ki-Pauri ghat, held every evening, is also worth experiencing.
RishikeshSituated a little further up the Ganges River than Haridwar, Rishikesh is considered to be the birthplace of yoga in India. It's renowned for its many ashrams. A Ganga Aarti is also held every evening in Rishikesh, at Parmarth Nitekan ashram, the predominant ashram there. Adventure activities, such as rafting, are popular as well. You'll also find a number of Hindu temples in Rishikesh.
So, what does all this mean for you?If you're a Hindu spiritual seeker, you'll find Haridwar to be the best place to visit. Why is this? Apart from its spiritual significance, the facilities at Haridwar cater mostly to Indians. There are plenty of snack stalls and cheap restaurants selling a variety of Indian food -- just the kind of thing Indians love! There's not a lot to do in Haridwar apart from visit temples, take a dip in the Ganges, and experience the aarti.
If you're a western spiritual seeker, you should head to Rishikesh. Plenty of foreigners go there to study yoga and it has much more of an international feel than Haridwar -- there are chilled out cafes serving western food, inexpensive guest houses full of travelers, book stores, clothes stores, healing centers (such as Reiki and Ayurveda), and of course yoga and meditation.
If you're not a spiritual seeker and just want to have a peaceful holiday, definitely choose Rishikesh. It's much more laid back and less crowded than rather chaotic Haridwar. It's possible to get out and enjoy the great outdoors there too.
Note: Something to keep in mind is that you won't find any alcohol or meat (including eggs) in Rishikesh or Haridwar, due to the holy nature of both places. If a strict vegetarian diet is not something you can deal with, you might not enjoy either place.