Neither is universally better; they suit different buildings. Cavity insulation is far cheaper where a suitable clear cavity exists, while external insulation delivers a bigger improvement, reduces thermal bridging and suits solid walls or houses where the cavity cannot be filled. A technical survey should decide which applies.
If the house has an unfilled cavity in good condition, pumped cavity insulation is usually the most cost-effective upgrade available, with minimal disruption. It cannot, however, be used where the cavity is too narrow, already filled, obstructed, or where the wall is exposed to severe driving rain without a suitable certified system.
External insulation costs considerably more but achieves a lower U-value, wraps junctions to reduce thermal bridging, and can be applied to solid walls where no cavity exists. It also renews the external finish, which can be an advantage on a tired façade.