I have both.
Both are printed on similar sized pages, about 18 inches high by 12 inches (24 inches opened) wide. The Times has rather more entries, including more smaller cities and the routes of roads and railroads. The National Geographic devotes more supplemental pages to picturing the topography of the earth and the ocean floors (although they are not absent from the Times). Each has a couple of pages devoted to the explanation of various projections used to portray a spherical earth on a flat page. Each devote a few pages to maps of the moon and maps of the heavens. The Times prints all it pages in color indicating altitude while the National Geographic prints political maps on white pages (with mountain ranges shaded in), making it a little bit easier to read place names at the cost of having to swap back and forth between a political map and a (generally smaller scale) topographical map to determine altitudes and land forms. The National Geographic has a number of satellite photos of continents and selected regions that the Times does not and it presents an overview of the ocean basins missing from the Times atlas. In the index, the Times includes the latitude and longitude for each entry while the National Geographic does not. The National Geographic includes a section with a thumbnail sketch of each nation’s history, showing their flag, population, area, prominent religions, etc. that is absent from the Times. The Times devotes a couple of pages to graphically comparing the sizes of continents, islands, drainage basins, lakes, and oceans that the National Geographic does not.
Rather than vague claims for quality, let me describe their separate presentations of Australia in the hope that that will give you a better idea.
The Times only shows an overview map of Australia as a section of Oceania on a (double page) map that includes New Zealand, New Guinea and the Solomons, Fiji, and Western Samoa.
The Times then “breaks up” Australia into three separate sections, showing a lot more detail regarding cities and roads (that is a little bit harder to read).
It presents city maps (all at 1:250,000 scale) for Canberra, Adelaide, Melbourne, Hobart, Sydney, Brisbane, and Perth. The Sydney map (for example) is just over 5 inches wide (at the bottom) and a bit over 9 1/2 inches high, extending from Bundeena and part of Royal National Park in the South to Ettalong and Pearl Beach in the North and extending West to Merrylands with the top of the map angling in, but still including Parramatta, Hornsby, Berowra, and Brooklyn. Major street outlines are shown, although only the most major streets are named.
The National Geographic has one (double) page devoted to Australia with smaller maps showing population clusters, land use and plant cover, resources and industry, major transportation routes, and environmental stresses.
The National Geographic then has a double page spread showing the landform of Australia.
It then has the political map of Australia (with whatever cities it can squeeze in to an 18 x 24 inch format) that also clearly identifies national parks.
The National Geographic presentation of the cities Sydney, Brisbane, Canberra, Melbourne, Adelaide, and Perth (no Hobart) are uniformly 3 3/4 inches square (meaning the scales differ between cities a little bit). The Sydney map (with about 1/3 the area of the Times map) begins in the ocean and extends West to The Oaks, Springwood, and Blue Mountains National Park and begins in the South, South of The Oaks, Campbeltown, and Cronulla (Bundeena is not shown although the map extends South for several miles) and to the North to Wiseman’s Ferry and Gosford. A few of the largest roads are indicated, although none are named.
I find that I use each atlas for different things. With luck, you can figure out what features would be more important to your mother.
Goode’s is a pretty decent atlas, as well. I don’t know whether I have their “top of the line” edition. Mine was a lot less expensive than either the Times or the National Geographic (and contains less information), but it is still a nice handy guide when I don’t need sufficiently detailed information to prompt me to haul out a 10 lb. book and clear off the kitchen table to open it up.