Hi Todd,
Ref. 3700 is the "Jumbo" Nautilus, made from the mid-1970s to sometime in the 1980s. It uses the cal. 28-255, without a seconds hand, from a JLC base movement. Ref. 3800 replaced ref. 3700, and uses Patek Philippe's cal. 330 SC. Ref. 3800 is in a smaller case than the Ref. 3700 and has center seconds. Ref. 3710, "new Jumbo" Nautilus, came out in 1998 using the cal. 330 SC IZR with a winding gauge at 11:30. Ref. 3710 returns to the "Jumbo" case size but is thicker than the original.
There are many variations on each of these, including case materials, dials, and jeweled versions. I should also mention the ref. 3900 mid-size and ref. 4700 ladies Nautilus, which use quartz movements. Refs. 3800, 3710, and 4700 are current models.
Best regards,
Stephen Sugiyama