It is a common practice for leaders to tap people they have liked or had success with in their previous company when they have to build a new team with a new employer. In fact, there are times when it's somewhat expected that bringing on a new leader from outside the company implies they have a team that they want to bring with them eventually. Should you be on that team? Should you follow your old boss to his/her new company to create the same magic you've created in the past?
While the familiar feeling and work style may seem like a bonus to you initially it may in fact be a limiting factor to you and your bosses growth potential. A great leader or boss will be someone who can grow and develop talent, not someone who clings to a previous protege that's dependable all the while knowing this person will be beholden to them for their growth and they essentially can make said boss look great with little to no intervention. It's convenient for the boss, but doesn't really test you to grow and expand. You're performing for the same "panel" over and over again. To truly grow your skills you need to impress multiple bosses over time who have different styles and show your ability to adapt and perform. And for your boss, they need to develop talent that is diverse in their skills and not rely on past performers to sure up their teams.
The temptation to "go with what you know" is certainly appealing, but you may short change yourself in the long run by not having to adapt to different leadership styles. In the end, you want to become the leader and nurture a team of your own someday that branches out and has an impact beyond your nest.
To use an NBA analogy, one of the most successful young coaches today is Steve Kerr of the Golden State Warriors. His mentor? Gregg Popovich of the Spurs who arguably created a dynasty for nearly 2 decades. The apple doesn't' fall far from the tree, but it must certainly become a tree of it's own.