The replacement of the JET carbon wall (C-wall) by a Be/W ITER-like wall (ILW) has affected the plasma energy confinement. To investigate this, experiments have been performed with both the C-wall and ILW to vary the heating power over a wide range for plasmas with different shapes. It was found that the power degradation of thermal energy confinement was weak with the ILW; much weaker than the IPB98(y,2) scaling and resulting in an increase in normalized confinement from H98 ∼ 0.9 at βN ∼ 1.5 to H98 ∼ 1.2−1.3 at βN ∼ 2.5 − 3.0 as the power was increased (where H98 = τE/τIPB98(y,2) and βN = βTBT/aIP in % T/mMA). This reproduces the general trend in JET of higher normalized confinement in the so-called 'hybrid' domain, where normalized β is typically above 2.5, compared with 'baseline' ELMy H-mode plasmas with βN ∼ 1.5 − 2.0. This weak power degradation of confinement, which was also seen with the C-wall experiments at low triangularity, is due to both increased edge pedestal pressure and core pressure peaking at high power. By contrast, the high triangularity C-wall plasmas exhibited elevated H98 over a wide power range with strong, IPB98(y,2)-like, power degradation. This strong power degradation of confinement appears to be linked to an increase in the source of neutral particles from the wall as the power increased, an effect that was not reproduced with the ILW. The reason for the loss of improved confinement domain at low power with the ILW is yet to be clarified, but contributing factors may include changes in the rate of gas injection, wall recycling, plasma composition and radiation. The results presented in this paper show that the choice of wall materials can strongly affect plasma performance, even changing confinement scalings that are relied upon for extrapolation to future devices.