Currently, in my organization, we have BI products built on top of a data warehouse implemented using PostgreSQL, following a snowflake schema architecture (fact and dimension tables). This structure has become extremely complex and hard to maintain. Updates are very costly, and I’m heavily dependent on a single person to keep it running. I’m considering moving to a cloud-based environment, such as AWS Redshift or Google BigQuery. Based on your experience, would migrating to one of these platforms help me move away from this complex snowflake architecture? Also, between the two solutions (AWS Redshift and Google BigQuery), which one would you recommend and why?

It is better to analyze from the problem perspective. Whether you need a Snowflake schema, star schema, or one big table, it needs to be analyzed based on the user requirements, data volume, query patterns, business asks, latency requirements, etc. Changing the database/platforms might not solve the issue if you need a sustainable solution.

Warehouse performance can be linked to multiple factors, like actual design vs blueprint design, how it has been built, underlying infrastructure and then comes technology choices. Before looking at a cloud data platform and thinking of moving to solve your problem, try to assess if your implemented design is scalable or not. 

Based on what you have described, it sounds like your problem is more the architecture or design of your database.  I don't think changing the underlying database technology is going to address your problem.  

Is your problem more related to the process you use to update your DW rather than the database itself?

What tools are you using to update your star / snowflake schema?