Love the TTSX for big stuff. From both my experience and in all I’ve read Barnes bullets perform best when pushed hard so I’ve pretty much restricted them to my .300win and .300wea with good results on big stuff. Took a 9ft Brown Bear with my .300wea/TTSX a few years back who I shot quartering toward me At about 75yards. Recovered the bullet from the hind quarter - perfect expansion and a lot of damage.
However, I think they are a bit too robust for standard speed rounds on deer, sheep and smaller. In my experience, less expansion, especially at med-long range. They’ll still work but feel softer Accubonds, ELD-X, and many tried-and-true cup & core bullets deliver more of their energy. My 30-06 and 6.5CM have accounted for many “bang-flops” or “down within sight” using Accubonds, ELD-X, and Hornady Interlocks. Have a lot of buddies who swear by Ballistic Tips on deer, sheep and smaller.