Same as Marrakai/Tony……..bigger bear, smaller bear……heart/lungs will kill but may run a fair distance. Break 'em down with a shoulder shot.
Seems that the 6.5 bullet offerings, that will feed in a 1903, are reported to be quite variable as to penetration and expansion? (Hornady 160 grain round nose)

6.5x54 MS at standard velocities with the 156-160 grain bullets ought to get the job done, but then our bears here are 200-350lbs….not huge.
- Mike