After having not spent Mardi Gras in a constant drunken stupor (purely for observational purposes) and having spent time in different areas of the city for the event, I can say there are two distinct sides to New Orleans Mardi Gras: Uptown and Downtown.
Parades are unquestionably the center of the Mardi Gras celebration. While many finish at Canal St. (for those unfamiliar with the city, this is the central downtown street that acts as a barrier between the business district and the ubiquitous French Quarter) they primarily run uptown. Here marks the distinction: the Uptown celebrations are more geared towards families. This is the optimal area for watching bands and floats, and catching the goodies krewes are tossing (don’t believe the stories, you really don’t have to do anything drastic to pick up some beads: honestly.) A good portion of the crowd is parents with children, and vendors run up and down the street selling light up toys and cotton candy. Not to say adults can’t enjoy; I had a blast, and especially recommend the Krewe of Muses parade, and Chewbacchus, the nerd parade. However, this is more wholesome fun than typically found more downtown and in the Quarter.
If Uptown is the place for Parade watching, Downtown is certainly the place for people watching. The Quarter has a few parades of its own, notably Krewe de Vieux, a satirical, less politically correct series of floats, with more of a DIY mentality. Down in the Quarter during Mardi Gras and the Days leading up to it, you can see people decked out in the most extravagant and weird of costume. At night, streets are packed, especially Bourbon Street, where the crowd is rowdy for beads and booze.
A good plan with Mardi Gras is a little bit of forsight, especially if driving is required. My personal advice would be to find a safe place to park, and give the car a break for a bit, as its impossible to navigate between people, parades and general madness.
If you’re new to New Orleans, remember there’s still ore to you’re visit than Mardi Gras! If you’re spending time Uptown and need a break, walk on over to Magazine street, where the crowds have mostly dissipated. Neighborhoods like the Bywater and The Marigny are a nice escape from Downtown insanity, where you can find unique dining and culture.
Final Conclusion: proper, formal Mardi Gras occurs Uptown. What outsiders perceive about Mardi Gras, the insanity and bacchanalia, occurs Downtown.