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 Europes place at the high-energy frontier during the coming decades.
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