The verdict
For a small team that wants to be live in a day and keep things simple, I'd pick Help Scout. It has a free plan, the inbox is easy to adopt, and it can replace both the shared mailbox and a separate knowledge base tool. If you need deep routing, workforce management, voice and an enterprise-grade set of features, pick Zendesk.
The trade-off in Zendesk is that useful AI and channel features sit above the entry plan, and several capabilities are add-ons, so ask for a full quote. In Help Scout, higher plans hold advanced workflows and single sign-on. Work out which plan holds what you need before you decide.