We present improved point-source catalogs for the 2 Ms Chandra Deep Field-North (CDF-N) and the 250 ks Extended Chandra Deep Field-South (E-CDF-S), implementing a number of recent improvements in Chandra source-cataloging methodology. For the CDF-N/E-CDF-S, we provide a main catalog that contains 683/1003 X-ray sources detected with wavdetect at a false-positive probability threshold of $10^{-5}$ that also satisfy a binomial-probability source-selection criterion of $P<0.004$/$P<0.002$. Such an approach maximizes the number of reliable sources detected: a total of 196/275 main-catalog sources are new compared to the Alexander et al. (2003) CDF-N/Lehmer et al. (2005) E-CDF-S main catalogs. We also provide CDF-N/E-CDF-S supplementary catalogs that consist of 72/56 sources detected at the same wavdetect threshold and having $P$ of $0.004-0.1$/$0.002-0.1$ and $K_sle22.9/K_sle22.3$ mag counterparts. For all $approx1800$ CDF-N and E-CDF-S sources, including the $approx500$ newly detected ones (these being generally fainter and more obscured), we determine X-ray source positions utilizing centroid and matched-filter techniques; we also provide multiwavelength identifications, apparent magnitudes of counterparts, spectroscopic and/or photometric redshifts, basic source classifications, and estimates of observed AGN and galaxy source densities around respective field centers. Simulations show that both the CDF-N and E-CDF-S main catalogs are highly reliable and reasonably complete. Background and sensitivity analyses indicate that the on-axis mean flux limits reached represent a factor of $approx1.5-2.0$ improvement over the previous CDF-N and E-CDF-S limits. We make our data products publicly available.
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