Both may describe something undesirable continues all the way, but Vする一方だ implies escalation, and Vするばかりだ does not. In this sense, you can replace Vする一方だ with （ますます／どんどん）Vするばかりだ.

If the verb already has a cumulative meaning, then the two expressions make no difference.

死傷者は増える一方だ。 = 死傷者は増えるばかりだ。
Casualties keep on increasing.

Otherwise, these two would not be interchangeable.

子どもはおびえる一方だ。 The child only gets more and more frightened.

 

子どもはおびえるばかりだ。 The child can do nothing but being frightened.

Both may describe something undesirable continues all the way, but Vする一方だ implies escalation, and Vするばかりだ does not. In this sense, you can replace Vする一方だ with （ますます／どんどん）Vするばかりだ.

If the verb already has a cumulative meaning, then the two expressions make no difference.

死傷者は増える一方だ。 = 死傷者は増えるばかりだ。
Casualties keep on increasing.

Otherwise, these two would not be interchangeable.

子どもはおびえる一方だ。 The child only gets more and more frightened.

子どもはおびえるばかりだ。 The child can do nothing but being frightened.

Both describe something undesirable continues all the way, but Vする一方だ implies escalation, and Vするばかりだ does not. In this sense, you can replace Vする一方だ with （ますます／どんどん）Vするばかりだ.

If the verb already has a cumulative meaning, then the two expressions make no difference.

死傷者は増える一方だ。 = 死傷者は増えるばかりだ。
Casualties keep on increasing.

Otherwise, these two would not be interchangeable.

子どもはおびえる一方だ。 The child only gets more and more frightened.

子どもはおびえるばかりだ。 The child can do nothing but being frightened.

Both may describe something undesirable continues all the way, but Vする一方だ implies escalation, and Vするばかりだ does not. In this sense, you can replace Vする一方だ with （ますます／どんどん）Vするばかりだ.

If the verb already has a cumulative meaning, then the two expressions make no difference.

死傷者は増える一方だ。 = 死傷者は増えるばかりだ。
Casualties keep on increasing.

Otherwise, these two would not be interchangeable.

子どもはおびえる一方だ。 The child only gets more and more frightened.

子どもはおびえるばかりだ。 The child can do nothing but being frightened.