We don't answer questions about which technology to use here, since it comes down largely to personal preference, compatibility with your studio's workflows, and the needs of an individual project.
There is an on-topic question here though about the differences between animating individual body part sprites versus pre-rendering your frames to a spritesheet and playing them back like a flipbook.
Individual body parts (this is often called 2D skeletal animation, particularly if you use hierarchies & constraints to help align the parts)
- Interpolate frames for smoother animations / control over playback speed
- Modify animations at runtime (eg. swapping body parts for character customization, blending/layering animations, using inverse kinematics to control things like looking/aiming angle, or adding dynamic animation like physics-driven wiggles)
- Smaller file size (typically)
- Author directly in Unity's built-in tools, or use middleware like Spine or Puppet2D
Exporting complete frames
- Simpler setup in your game engine (typically) - all you have to do is display the right frame
- Exact results - the frames you export are the frames you see
- Freedom to vary the content as much as you want from frame to frame - you can even hand-draw each frame uniquely (compare to animating body parts, where you typically re-use a collection of shapes with a limited set of transformations)
- Author in Flash or other animation program and export an image sequence or spritesheet.