Same Data, Two Penalties, Two Winners

Both prefer $\mathbf{w}_B$: it has the lower training error and the smaller penalty, so neither comparison is close.

Ridge prefers $\mathbf{w}_A$ ($0.90$ vs $1.00$) and Lasso prefers $\mathbf{w}_B$ ($1.00$ vs $1.30$).

Both prefer $\mathbf{w}_A$: two of its three weights are exactly zero, so it is penalised less under either norm.

Ridge prefers $\mathbf{w}_B$ ($1.00$ vs $1.30$) and Lasso prefers $\mathbf{w}_A$ ($0.90$ vs $1.00$).