I have also read that in a few different places. My knowledge comes from serving on two different brigs, and reading seamanship in the age of sail and other publications. Lady Washington is about as weatherly as the "square rigger standard" for those days as is commonly publicized, she will sail about 65 to 70 degrees close hauled, and her speed will be hampered a fair bit compared to the same wind levels on a beam or broad reach. The main physical factors affecting how well a square rigger sails to windward are how sharp the yards can be braced, which differ's ship to ship, and how fine the entry of her bow is for taking a head sea. Lady was a merchantman and has a very round bow, therefore she sails pretty well close hauled in a mild to moderate sea state, but if there is a heavy head sea her ability to sail to windward is dramatically reduced. Niagara however, can brace her yards much much sharper than Lady due to larger and different rigging geometry, and she is much longer on the waterline with a very very fine clipper bow. Niagara's capability to sail to windward at speed is head and shoulders above Lady Washington. I recall a day sailing on lake Erie, single reef in the topsails, I was at the tiller steering full and by (as close as she would lie to the wind without luffing,) it was blowing about 20 knots and I was stunned, Niagara was charging along at over 9 knots right up against the wind, the anemometer read 55 degrees, and sometimes dipped a degree or two lower, her clipper bow sliced through head sea's with ease. Steering Niagara with a decent wind is one of my most treasured memories. I love both brigs equally, but for close hauled sailing capacity Niagara has, sharper traverse of yards, longer waterline length contributing to higher hull speed, and a clipper bow to cut through head seas.
Hope this answers your question. Here is Niagara tearing along right up against the wind. She does have disadvantages.. She was built quickly and designed for one decisive battle, the battle of lake Erie. She was never designed as an ocean going warship and has significantly lower freeboard than Lady, which means she will reach deck edge immersion and downflood sooner, she was also built with a very lofty rig, lots of sail area for her hull design, the result is an extremely powerful low and moderate wind performer, able to ride out heavy weather on the lakes, but never designed to stand up to ocean sea states.