Recently used .blender export to great effect. No doubts.
.Babylon is really excellent. But yeah -> had to muscle Blender to figure it out.
Precisely exporting animation was tough... but once solved, clear sailing for subsequent animations.
This is rocket-science. btw.
1) Got to go step by step until you get Blender figured out.
2) Example: Object > Apply > Location & Rotation & Scale (or every animation will spaghetify - until an animation needs reference to 0,0,0 -> then don't! ). memorized. Explodes lots of exports.
3) Yep, skeletons not always be passing through (I remember) -> at first. debugger; Just do it. Because ....
4) Sometimes you accidentally export multiple skeletons (blender) and the skeleton at  is not the one you need. Same with meshes. Gotta a step in and look sometimes.
5) Other times, if you put code in the callback, that fails, borks executions... like animations. Looks like bad export but not... as Wingnut points out.
6) Exporting Animations from Blender to .babylon - gotta get crafty to be advanced. Example: Made 7 (unusual) IKs in blender animating, but none after export... the 8th worked. Troubleshooting only way.
7) Browser Refresh is cached for .babylon. So either manifest switch permissions so refresh reloads export updates... (idk), OR update the file version every export. Often hits 10. nbd.
8) ...100 problems. 99 fixed in Blender. Example: do not export camera/lights. Others me being wrong... but .babylon exporter pretty solid. Clapping... JCP.