  In this paper we fit two models of Early Dark Energy (EDE) (an increase in
the expansion rate before recombination) to the combination of Atacama
Cosmology Telescope (ACT) measurements of the Cosmic Microwave Background (CMB)
with data from either the WMAP or the Planck satellite, along with measurements
of the baryon acoustic oscillations and uncalibrated supernovae luminosity
distance. We study a phenomenological axion-like potential ('axEDE') and a
scalar field experiencing a first-order phase-transition ('NEDE'). We find that
for both models the 'Planck-free' analysis yields non-zero EDE at > 2 sigma and
an increased value for $H_0 \sim 70-74$ km/s/Mpc, compatible with local
measurements, without the inclusion of any prior on $H_0$. On the other hand,
the inclusion of Planck data restricts the EDE contribution to an upper-limit
only at 95% C.L. For axEDE, the combination of Planck and ACT leads to
constraints 30% weaker than with Planck alone, and there is no residual Hubble
tension. On the other hand, NEDE is more strongly constrained in a Planck+ACT
analysis, and the Hubble tension remains at $\sim 3\sigma$, illustrating the
ability for CMB data to distinguish between EDE models. We explore the apparent
inconsistency between the Planck and ACT data and find that it comes (mostly)
from a slight tension between the temperature power spectrum at multipoles
around $\sim 1000$ and $\sim 1500$. Finally, through a mock analysis of ACT
data, we demonstrate that the preference for EDE is not driven by a lack of
information at high-$\ell$ when removing Planck data, and that a LCDM fit to
the fiducial EDE cosmology results in a significant bias on $\{H_0,\omega_{\rm
cdm}\}$. More accurate measurements of the TT power spectra above $\ell\sim
2500$ and EE between $\ell \sim 300-500$ will play a crucial role in
differentiating EDE models.
