Here are the two pairs of navy pants side by side. I ended up getting the petite length from Old Navy, an option that is not available from Lilly Pulitzer. Both pants are a deep navy color and are fairly structured, considering that they are basically luxury leggings, if such a thing exists.
For the waistband, the Old Navy pants are the winner. The waistband is thicker and sits a little bit higher on the waist than the Lilly Pulitzer pants. Neither waistband twists or turns while wearing the pants.
Both pants have a center seam running down the front. The option from Old Navy has some side seams, too. Overall, the fabric of the Travel Pants is more substantial and stronger than the Old Navy pants. Both pants are very figure flattering and are completely opaque in addition to hiding any flaws or bumps.
The petite length of the Seamed Ponte Knit Pull On Pant from Old Navy is a good thing for me. I'm 5'4" and the Travel Pants scrunch up a little bit at my ankle. They're not overly long, but the petite option is really the better choice.
In all, I love both pants. My favorite pant is the Travel Pant, but I'd probably choose the Old Navy version in basic colors like navy and black. Then I could purchase the Travel Pant in more unique colors like charcoal gray and almond. The option for petites (and tall!) is fabulous for special sizes. Old Navy almost always has a deal for 20% off a purchase or more, so you can pick up their pants for about 75% less than the Lilly Pulitzer version. I say go for the less expensive option in basic colors and splurge on a bright pink Elsa or Murfee scarf.