Charting the European Course to the High-Energy Frontier

We review the capabilities of two projects that have been proposed as the next major European facility, for consideration in the upcoming update of the European Strategy for Particle Physics: CLIC and FCC. We focus on their physics potentials and emphasise the key differences between the linear or circular approaches. We stress the uniqueness of the FCC-ee programme for precision electroweak physics at the $Z$ peak and the $WW$ threshold, as well as its unequalled statistics for Higgs physics and high accuracy for observing possible new phenomena in Higgs and $Z$ decays, whereas CLIC and FCC-ee offer similar capabilities near the $t \overline t$ threshold. Whilst CLIC offers the possibility of energy upgrades to 1500 and 3000 GeV, FCC-ee paves the way for FCC-hh. The latter offers unique capabilities for making direct or indirect discoveries in a new energy range, and has the highest sensitivity to the self-couplings of the Higgs boson and any anomalous couplings. We consider the FCC programme to be the best option to maintain Europe's place at the high-energy frontier during the coming decades.