A few more details about the flavor(s) of absinthe:
If you're game, pick a bar with a good selection. I like Pravda! (1113 Decatur St., between Ursulines and Gov. Nicholls).
Any of these absinthes would make a fine introduction: Obsello, Marteau, Pacifique, Nouvelle-Orléans, Eichelberger 68 — all "vertes" (green in color). The bar might also stock La Clandestine and Kübler — both "blanches" (clear).
These absinthes don't require additional sweetening, but if you like a sweet drink, just remember to ask the bartender not to light your sugar cube:
1113 Decatur St, New Orleans, LA 70116
in basic terms, a sazerac tastes like a smooth whiskey that's slightly sweet with hints of other flavors (anise, citrus). absinthe, in the traditional sugar/water drip preparation, tastes like liquefied black licorice.
that's how the two drinks strike me, but i'm no connoisseur. i'm sure others with more experienced, nuanced palates will chime in.