I'm hard-pressed to think of any advantages to running Redis as a sidecar. I would always run it as a separate deployment (or stateful set if persistence is enabled) with a separate service.

If Redis is in its own pod then:

• If your application has multiple replicas, they'll all share the same Redis
• When you redeploy your application, it doesn't also terminate and restart Redis
• If persistence is enabled for Redis, you don't need to configure your application pods with the persistent storage

Given Redis's overall capabilities (principally in-memory storage, limited data-type support), simply storing this cache data in singleton objects in your application would be more or less equivalent to running Redis as a sidecar (one copy of the cache data per pod, data is lost when the pod is deleted).