No. A larger gamut plot in ColorSync Utility does not show that a monitor is currently displaying colours accurately. The plot represents an ICC profile, not a new measurement of the screen. Selecting a larger profile is not a repair for a visible colour mismatch.

This is an advanced colour-management check for someone comparing identified display, printer or working-space profiles. For an ordinary problem such as a photo looking different on two screens, first establish which file, application, display settings and profiles are involved. A plot alone cannot identify the cause.

Compare the intended profiles

1. Open ColorSync Utility on the Mac and choose Profiles. Expand the relevant group and select the first profile.
2. Use Open if you need to inspect its identity or details. A working-space profile should not be mistaken for a measurement of a particular monitor.
3. In the plot menu, choose Hold for Comparison, then select the second profile. The held surface appears lighter.
4. Rotate the plot to inspect different regions. Use Clear Comparison when finished.

Use the comparison to choose the next check

The view can show where the two profiles describe different colour ranges. It does not supply a reliable coverage percentage from a single screenshot, or prove how the complete document-to-display or document-to-printer workflow is behaving.

If you selected an unexpected profile, check which profile the actual application or output workflow requires before changing settings. If the concern is present-day display accuracy, arrange a measurement-based assessment of that display and its intended settings. For print delivery, follow the printer or project owner's specified profile and proofing process.

When asking for help, provide the two profile names and origins, the file and application concerned, and what looks wrong. That is more useful than reporting only that one coloured shape is bigger.

Source: Apple: viewing and comparing colour profiles.