I recently argued with a coworker about the differences between ibuprofen, the compound use in drugs like Advil, and naproxen sodium, the active compound in Aleve. I asserted to my coworker the drugs are essentially the exact same, but her unscientific mind could not believe me. So I will explain the biochemical mechanism of these drugs and why they both relieve pain in the same manner.
Pain sensation in our bodies is caused by our cells reacting to damage and responding by synthesizing compounds that alert us of the damage which is our perception of pain. The compound synthesizes are prostaglandins and are always expressed in response to tissue/cell damage. Blocking the generation of prostaglandins is the key element to inhibiting the sensations of pain. The enzyme that generates prostaglandins is the cyclooxegenase-2, or COX-2. There are two isoforms of the COX enzyme though COX-1 and COX-2. So in understanding why naproxen sodium and ibuprofen are the same one must understand they both are nonselective inhibitors of the COX enzymes. That being said both naproxen sodium and ibuprofen effectively block both COX-1 and COX-2. This is why they are essentially the exact same in drug effectiveness despite what some people seem to prefer, Aleve vs. Advil.
However because both drugs are nonselective they can cause problems throughout the body when inhibiting the COX-1 enzyme. The COX-1 enzyme is important in the production of platelets required for coagulation of blood. This is why people will use both ibuprofen and naproxen sodium as an anticoagulant. Using either drug over a period of time will result in blood thinning and the ability to clot blood effectively. Red blood cells (RBCs) generate platelets using the COX-1 enzyme, but cannot regenerate extras of the enzyme because the nucleus is lost in all RBCs. For this reason both naproxen sodium and ibuprofen will inhibit COX-1 in RBCs permanently until the cell dies and is replaced.
Overall the ibuprofen and naproxen sodium are effectively the same. Here you can find a few links to research papers that will back my reasoning. Trends from different studies go back and forth on which drug was prefered by the patients tested. Nonetheless either drug will get the job done.