Although temperature conditions (cold, followed by warmth, followed by cold) can produce poor flavours, and neither vegetable is at its best when it is old and tough, I think the most likely cause is carrot root fly problems. The carrot fly affects both vegetables.

The following quote from the Acta horticulture site gives more possible explanations:

"Bitter taste and turpentine-like taste are undesirable in production of Umbelliferous crops. Carrots with bitter taste can contain large amounts of 6-methoxymellein or isocumarin or 3-methyl-6-methoxy-8-hydroxy-3,4-dihydro-isocumarin. Many different terpenes in carrot cause turpentine-like taste. Usually terpenes give a desirable taste to carrots, but in high concentrations can give undesirable taste. Factors influencing undesirable taste include genetics, growing conditions, diseases and insects, post-harvest handling and storage atmosphere."

Just try again this year and you will probably find that both vegetables will be fine.