There isn’t one universally “best” simulator for mobile manipulation policy training—it depends on whether you care most about speed, photorealism, differentiability, contact fidelity, or sim-to-real transfer. But if I had to give a practical answer:

Best overall for policy training

NVIDIA Isaac Sim / Isaac Lab

• Strong choice for mobile manipulation + RL / imitation learning
• Good GPU acceleration and scale-out training
• Solid support for robots, sensors, navigation, and manipulation
• Better modern ecosystem for training policies than many older robotics simulators
• Especially attractive if you want sim-to-real workflows

Best if you want maximum training throughput / simpler RL

MuJoCo

• Very fast and stable for control
• Great for learning locomotion/manipulation policies
• Excellent for research on dynamics/control
• Less focused on realistic perception, full mobile manipulation stacks, or rich 3D environments

Best for ROS-centric robotics workflows

Gazebo / Ignition Gazebo

• Good if you want integration with ROS/ROS 2
• Widely used in robotics
• Better for systems-level testing than large-scale policy training
• Usually not as fast or RL-friendly as Isaac Sim/MuJoCo for large-scale training

Best for visual realism / perception-heavy tasks

Isaac Sim or Unreal-based environments

• If your policy uses RGB/RGB-D and you care about photorealistic rendering and domain randomization, Isaac Sim is often the strongest practical option.

If you want a lightweight, flexible research platform

PyBullet

• Easy to use, popular in research
• Decent for prototyping
• Not as strong as Isaac Sim or MuJoCo for serious large-scale training or realism

My recommendation by use case

• Policy training for a mobile manipulator with perception: Isaac Sim / Isaac Lab
• Fast low-level control policy learning: MuJoCo
• ROS integration and robotics system testing: Gazebo
• Quick prototypes / experimentation: PyBullet

Short answer

If your goal is training policies for a mobile manipulation robot, the most generally strong modern choice is:

NVIDIA Isaac Sim + Isaac Lab

If you want, I can also give you a decision table comparing Isaac Sim, MuJoCo, Gazebo, and PyBullet specifically for mobile manipulation training.