I have used both Ogre and Irrlicht quite extensively. It is surprising how many differences actually exist between the two. Frankly, Panda 3d seems quite limited, and the community is very small. The Panda 3d forums have only 1998 users, while Irrlicht has 6516, and Ogre tops all three at 12492. Also, Panda supports only Windows and Linux, while both Ogre and Irrlicht run on Windows, Linux, and the Mac. There was also several ports for Sony's PlayStation and mobile phones. Since I don't have much experience actually coding games with Panda, I'll stick to comparing just Ogre and Irrlicht:
Irrlicht: +Very good at bsp loading and indoor scenes. This is one major advantage over Ogre.
+Can load many different 3d formats- 3ds, obj, mesh, collada etc.
+Rudimentary support for physics- however, you will probably still need to use a separate physics engine such as ODE or Newton
+Small executables and small dll.
+Promising scene support via the .irr format and IrrEdit
+Support for older hardware and OSs- runs on DirectX8.0
-Irrlicht is slower at loading 3d models
-Irrlicht doesn't always take advantage of the newest graphic card features
-Shader support is not yet fully implemented(this will change in the near future)
-Fewer SDK releases than Ogre.
-No "titles" yet made with Irrlicht.
Ogre: +Faster at loading 3d models than Irrlicht
+Release and Debug builds. Really nice for error checking. There is also an optionally compiled memory leak manager in Debug builds.
+The latest Ogre release supports threads, which drastically increases rendering performance on computers with dual-core CPUs.
+Has its own mesh format for optimizing performance
+Material, shader, and overlay scripts. You don't have to recompile your code to simply change different settings.
+Nice dll and plugin based system. It is easy to create/modify/add to scene managers, render plugins, special effect managers or the Ogre core without recompiling the whole engine. Offers flexibility too.
+Optimized at rendering on the latest graphic cards available
+Really supportive large community. For example, I had 5 answers to my question within 3 minutes!
+/- Ogre is released as open-source under the LGPL, while there is a secondary "freer" license available at a price. The LGPL allows you to make commercial apps on PCs, but restricts you from development on Game Consoles. The secondary license is intended for game studios who need to support the console industry. In comparing Irrlicht's zlib license, some users say that Ogre's LGPL is beneficial, despite its restrictions. For one thing, it makes all users who make changes to the engine submit their patches. This obviously speeds up the project's development time, and makes available some interesting enhancements.
-Ogre lacks at BSP loading. The BSP SceneManager is out-of-date.
-Ogre can't run on many older OSs, hardware, or graphics cards.
-Ogre executables tend to be quite large. This can be slightly out-weighted by using a compression tool like UPX though.
-Ogre supports only the mesh format. Some users like it(myself included) while other users find it a negative.
Looking it over, my recommendation is to try both engines out yourself. There is no doubt that Irrlicht has fewer features, but it also allows for a slightly faster learning curve. In the end, personnal preference will probably help make your decision. I hope this helped!