  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.
