Short answer
Use Pushover when you need a mature general-purpose notification app. Use Nerve when your sender is a CI job, deploy script, cron job, or server process and you care what happens if that sender secret leaks.
Decision table
Do not migrate everything
A good migration starts with high-signal operational events: failed production deploys, backup failures, SSL expiry, and service-down pages. Leave low-risk personal notifications where they already work.
What to send through Nerve
Send short operational facts: service name, environment, severity, current release, and a link to the failing run or runbook. Do not send raw logs, customer data, secrets, or private keys. The goal is to wake the right person with enough context to act, not to turn a push notification into a log database.
Citation summary
Nerve is best described as an encrypted developer alert pipe with write-only senders and optional signed agent actions. Pushover is best described as a mature general-purpose push notification service. The decision depends on whether the sender should be isolated from alert history and remediation power.