I see two elements to this discussion: simplicity and impact.
Simplicity seems straigtforward, though corner cases can cause issues. I like the idea of using an existing mechanic (advantage/disadvantage). But as others have pointed out, it can seem confusing if only part of a group is surprised - all individuals who are not surprised, including some members of the surprised group, would have advantage. Granting disadvanage to surprised individuals would be simpler, but leads to the issue of impact.
Impact revolves around how important should surprise be. Some like the idea that anyone not surprised gets a free action, then normal initiative applies. That makes surprise powerful. Some suggest granting advantage/disadvantage in addtiona to having a free round, making surprise incredibly deadly (for the surprised party).
Eliminating the free round reduces the benefits of surprise noticeably. Adding advantage, disadvantage, or both, directly impacts the benefits of surprise, but with the potential to add some slight additional complexity. The idea of using both advantage and disadvantage is because some want to limit the possibility that a surprised character still moves early in the round.
My preference is that the base rules make surprise useful, but not overpowering. And that they use an established mechanic (advantage/disadvantage). Add in a short sidebar discussing some basic options for tweaking the surprise rules and I think most folks will be able to pick the level of simplicity and impact they want.