From the Battlepack wikia page:
Battlepacks are content packages featured in Battlefield 4 and Battlefield Hardline, as well as the upcoming Battlefield 1 that add a new layer of persistance and element of chance to multiplayer.
This would imply that receiving a battlepack is based on chance rather than skill.
Here's another article that suggests you just get them randomly:
Unlike in the past, Battlefield 1 players can earn battlepacks simply by playing the game.
Here's another that explicitly says it's random:
The chances of you receiving one at the end of a match is random; we've heard some players not getting any for a number of hours, while we got our first at the end of our second match, so it's a case of keeping playing until they start landing in your lap.
Based on this article, it sounds a lot like the case system in CS:GO.
Battlepacks are being simplified to a degree. There's now only a single type--a plain old Battlepack--you'll earn by playing.
Although, a major difference between cases and battlepacks is here:
Weapon skins or bonus items you're not interested in can be broken down into Scrap, a currency you can use to buy more Battlepacks, including Enhanced and Superior versions. These Battlepacks can only be purchased with Scrap and guarantee you'll receive higher-rarity weapon skins. In other words, destroying things you don't want gives you a better chance to unlock weapon skins you'd otherwise be less likely to earn through a standard Battlepack.