A trampoline or a bounce house can help kids have fun while burning off energy. However, a trampoline is much simpler than a bounce house. It only provides an avenue for jumping, even if you can add a couple of fun accessories to the mix (like a basketball hoop). On the other hand, a bounce house provides tons of fun features like a slide and ladder.
A trampoline is easier to set up when it comes to ease of use. You need to inflate and deflate a bounce house every session. Cleaning is also a challenge with a bounce house because it has many nooks and crannies.
As for safety, a bounce house is much safer for younger kids because it has bouncy walls for security. While you can install nets and pads to make your trampoline safer, it's still not the best option for children younger than 7 years-old.