Both of them are good and got their own flavors. If it is your first time, then make it to North Goa. Don't even think about visiting South goa on your first visit.
You'll find plenty of advises on this but dont give it a second thought. You always had that specific picture of Goa in your mind. Be it from the movies, internet images or your friends album. It always seems special and a wonderful place to visit.
Think about the movies like Dil Chahta Hai, Socha Na tha & movies like Finding Fanny, Drishyam? Do you recall any difference between the Goa portrayed in DCH and that in Drishyan. That's what North and South Goa is.
You always have imagined Goa as a party zone, known for lovely beaches, a place to hang around with loved ones, chilling out with beer, sitting and partying or atleast enjoy it by being among partying people. Apart from it, lot of travelers around and great markets with all resource availability is always good when you visit any town.
Now you look at some pictures below,
And the following pictures now.
If you find the first part of pictures better, you belong to North Goa.
South Goa is ideal to visit if you have been to North Goa before couple of times atleast. Lesser people around, limited markets, shacks are closed by 11 or 12 max if people are there. You will spend your late evenings usually at your place, around silent beaches mostly.
But in the north, you will enjoy a great nightlife. Not to forget several day activities including boat tours, water sports and what not. It is busy, crowded but a great fun. So I'll suggest you to visit North Goa and don't even think of South Goa.
There are places in North Goa which can match with South Goa beaches but opposite is not true. If you want peaceful, cleaner and beautiful beaches, head towards Anjuna stretch and stay at Arambol beach. Candolim is another pretty beach and Panjim is merely 15 kms where you can easily drive on your rented bikes.
To conclude, lot of options & variation is available in North Goa. Peace, parties, people, flea markets, watersport, forts, tattoos, awesome streets. You can switch to different places as per your choice in North Goa.
Whereas in South Goa, you'll find cleaner beaches (cleaner than Baga and Calangute beaches. Otherwise, Candolim, Vagator, Morjim, Arambol in north are much cleaner), pretty sunsets and peaceful holidays but you'll miss the party.
Final words, you can stay among people and still get away to find peace in North Goa but you can’t simply have that typical fun in South.