  (Abridged) We present an analysis of X-ray observations made of the Galactic
supernova remnants (SNRs) HB21 (G89.0+4.7) and CTB 1 (G116.9+0.2), two
well-known mixed-morphology (MM) SNRs. We find a marked contrast between the
X-ray properties of these SNRs: for HB21, the extracted ASCA spectra of the
northwest and southeast regions of the X-ray emitting plasma can be fit with a
single thermal model with marginally enhanced silicon and sulfur abundances.
For both of these regions, the derived column density and temperature are
N_H~0.3x10^22 cm^-2 and kT~0.7 keV, respectively. No significant spatial
differences in temperature or elemental abundances between the two regions are
detected and the X-ray-emitting plasma in both regions is close to ionization
equilibrium. Our Chandra spectral analysis of CTB 1 reveals that this source is
likely an oxygen-rich SNR with enhanced abundances of oxygen and neon. The
extracted ASCA spectra for the southwestern and northeastern regions of CTB 1
cannot be fit with a single thermal component. Based on our fits to these
spectra, we derive a column density N_H~0.6x10^22 cm^-2 and a temperature for
the soft thermal component of kT_soft~0.28 keV. The hard emission from the
southwest may be modeled with either a thermal component (kT_hard~3 keV) or by
a power law component (Gamma~2-3) while the hard emission from the northeast
may be modeled with a power law component (Gamma~1.4). We have also extracted
ASCA GIS spectra of the discrete X-ray source 1WGA J0001.4+6229 which is seen
in projection toward CTB 1. These spectra are best fit using a power-law model
with a photon index Gamma=2.2^{+0.5}_{-1.2} which is typical for featureless
power-law continua produced by rotation-powered pulsars. This source may be a
neutron star associated with CTB 1.
