The two filmmakers are similarly prolific. Between 1984 and 1991, Hughes served as writer, director, or producer -- and sometimes all three -- on a whopping 14 movies. Apatow, meanwhile, has his name on 15 films just since 2005, three as director (The 40-Year-Old Virgin, Knocked Up, and the upcoming Funny People), and the rest as writer or producer. Granted, a producer (especially "executive producer") doesn't always have much influence on the actual creative content of a film, but it's not hard to look at something like, say, Superbad, and see Apatow's fingerprints.
Apatow-produced films tend to rely less on tight screenplays and more on improvisation and horsin' around -- but Hughes dabbled in that, too, particularly when working with people like Steve Martin and John Candy (Planes, Trains & Automobiles) or Chevy Chase (the Vacation movies). There are supposedly enough deleted scenes from Planes to make a three-hour version of the film, an idea that should sound familiar to Apatow fans.
On a deeper level, the films by Apatow and Hughes tend to focus on teenagers or immature adults whose lives are altered either by regular slice-of-life stuff (losing one's virginity; graduating from high school) or major events (unplanned pregnancy!). The films are always comedies, and often sarcastic and caustic (and, with Apatow, incredibly vulgar), yet there's always a tender side, too. Their films have heart.
Technically, Apatow and Hughes even worked together on Drillbit Taylor, which Apatow produced and which was based on an old story by Hughes (who was credited as "Edmond Dantes").
But there are differences, too. Hughes is reclusive and avoids interviews; Apatow is outgoing and omnipresent. Hughes worked almost exclusively in the PG and PG-13 realms, while Apatow is usually rated R (and a hard R at that). Hughes' films felt simpler, more teen-friendly -- but then again, teens have changed a lot since the mid-1980s. Kids under 17 might technically be barred from seeing Apatow's films, but they see them anyway, and they relate to them.
Finally, John Hughes and Judd Apatow both have four-letter first names starting with "J," and six-letter last names. I don't know what more proof you need.
I leave it to you. Is Judd Apatow this generation's John Hughes? If not, does that title fall to someone else? Or was Hughes a hack who wasn't worth emulating anyway? (Note: If that's your position, may the gods have mercy on you.)