Recruiting selectivity is not a single ladder where every boutique is automatically easier than every MBB office. Smaller firms may hire very few people and can be much more specific about industry, geography, or prior experience.
Your profile may fit the broad generalist MBB model better than a boutique looking for a particular background. It can help to revisit how you tailor your consulting resume for each firm's actual work.
Tailor the application more aggressively when the firm's work is specialized. Make the relevant experience obvious instead of assuming the recruiter will infer the connection.
Finally, treat each process independently. Passing one prestigious screen does not guarantee another firm wants the same profile, especially when its hiring class may be tiny.