This study tests the relative amount of cognitive effort required for Spanish language processing by L1-dominant speakers (Spanish-raised bilinguals, SRBs), heritage speakers (HSs) and late second-language learners (English-raised bilinguals, ERBs). In a dual-task study, three groups of bilingual Spanish speakers were presented concurrently with a linguistic and non-linguistic task, each at three levels of difficulty. When responding to the non-linguistic task, which required concurrently processing and encoding in memory a Spanish-language phrase, SRBs were, on average, most accurate and ERBs least accurate. This suggests a three-way difference between SRBs, HSs and ERBs in the amount of cognitive resources required for language processing in the target language, highlighting HSs’ unique developmental trajectory. Results further suggest that accuracy on the non-linguistic task was reduced for all groups when the concurrent linguistic stimulus was of higher syntactic complexity, suggesting that more complex linguistic structures require more cognitive resources regardless of language background.