Use employee management software when the unresolved work involves employee records, manager approvals, onboarding, or personnel documents. Cloud accounting software is usually the better starting point for invoices, expenses, bank reconciliation, and financial reporting. Adding HR software makes sense when those accounting functions work but people-related work still depends on scattered files and repeated follow-up.
This is usually a decision about where to manage employee information, rather than whether to stop using accounting software. A business may need both. Payroll features and HR add-ons can blur the boundary, so examine the actual capabilities included in your current plan before buying another system.