This is a timing and depth question, not a values question. Both formats produce useful output; they serve different situations.
Run a brand sprint when: you have a hard external deadline (fundraise, product launch, board presentation, rebranding before a market entry), when your leadership team already has strong market knowledge and the constraint is synthesis rather than discovery, or when your current positioning is so misaligned that something working is more valuable than something perfect.
Run a full brand strategy engagement when: you have time to do it properly (3 to 6 months), when the business is at a major strategic inflection point that requires deep competitive analysis and external customer research, when there are significant internal disagreements about direction that need structured facilitation over multiple sessions, or when the visual identity and website build are both in scope and need to be sequenced carefully.
In practice, most B2B companies at Series A through C are better served starting with a sprint. The compressed format forces decision-making in a way that longer engagements sometimes don't — there's less time to second-guess or to defer difficult calls. The sprint also produces something that can be tested: you can run the new messaging against actual ICP buyers before committing to a full identity and website build.
The hybrid model that works well: run a sprint to establish positioning and messaging, validate with a small campaign or direct outreach, then use the validated positioning brief as the input for the full brand identity and website engagement. That sequence is faster overall and produces better work at each stage because each stage is building on tested rather than assumed foundations.