Why is my vegetable stock bitter, but the chicken stock not? I have exactly the same procedure and ingredients for cooking vegetable and chicken stock - of course, the latter contains chicken meat, which is the only difference. 

The ingredients I put into my stock are:


onion, 
a few garlic cloves, 
two carrots, 
celeriac, 
parsley root,
leek,
spices: bay leaf, allspice and peppercorns. 


Simmer time - about 2 hours.

It quite often happens that my vegetable stock is bitter, but it never happened with a chicken stock. I read here and there that vegetable stock shouldn't be cooked for long - even 45 minutes should be enough, and if simmered for too long it may become bitter. However, chicken or any other meat stock recipes call for a much longer time, and bitterness should not be a problem.

Thus, why is there a risk of vegetable stock becoming bitter, while it is not that much of a problem for a meat stock?
I notice that your recipe doesn't include any salt. That's important, because salt decreases the sensation of bitterness. Chicken contains a certain amount of salt, and I suspect that's making the difference. (The "umami" -- brothy -- taste of chicken may also decrease the sensation of bitterness, though as I understand it there's still some disagreement about that.)

Try mixing 1/8 tsp of salt into one cup of your vegetable stock as a test. I suspect that'll decrease the bitterness to a comparable level.

Oh, and if you want to make your stock less bitter without making it more salty, use parsley stems and leaves instead of parsley root, and celery (including leaves) instead of celeriac. Those two roots will be the primary sources of bitterness.

Incidentally, I very much approve of you not salting your original stock, and instead salting whatever you use it in. Unsalted stock is more flexible, and is more forgiving if you decide you need to concentrate it.