Is the word doendo the same in Brazilian and European Portuguese?

No

While the word "doendo" (the gerund of the verb doer) exists in both dialects and carries the same meaning ("hurting" or "aching"), there is a significant difference in typical usage and grammar.

In Brazilian Portuguese, the gerund is the standard way to express an ongoing action or a continuous state. A Brazilian will naturally say "está doendo" (it is hurting).

In Continental Portuguese, the gerund is much less common for describing continuous actions. Instead, Portuguese people naturally use the construction a + infinitive. Therefore, to express the same idea, a person from Portugal would typically say "está a doer."

Brazilian Portuguese Examples

1. Minha cabeça está doendo muito hoje. (My head is hurting a lot today.)
2. Meu dente está doendo desde ontem à noite. (My tooth has been hurting since last night.)
3. A barriga dele está doendo por causa da comida. (His stomach is hurting because of the food.)
4. Sinto o meu braço doendo depois do treino. (I feel my arm hurting after the workout.)
5. O coração está doendo de tanta saudade. (The heart is hurting from so much longing/missing someone.)

Continental Portuguese Examples

1. A minha cabeça está a doer muito hoje. (My head is hurting a lot today.)
2. O meu dente está a doer desde ontem à noite. (My tooth has been hurting since last night.)
3. A barriga dele está a doer por causa da comida. (His stomach is hurting because of the food.)
4. Sinto o meu braço a doer depois do treino. (I feel my arm hurting after the workout.)
5. O coração está a doer de tanta saudade. (The heart is hurting from so much longing/missing someone.)