Memcached is probably more suited for storing html/json fragments than Redis. The Dalli[0] memcached driver does compression for you.
There are benchmarks on the project that illustrate the performance edge it has over Dalli as well.
Redis provides multiple databases (0-16) for just this situation. Use one db for caching, another for Sidekiq, and another for ad-hoc tasks. Redis can also be configured to evict entries with an expiration first, which means cached data will be cycled through while the important bits linger safely.