The funny thing is that most bullets will work most of the time. This is especially true at the ranges where most elk are taken.
That said, I tend to be very selective about my bullets. I wan one that will work reliably from a few feet to as far as Id be willing to take a shot under perfect conditions (600 yards, the limit of my practice). That means reliable but controlled and limited expansion, with good weight retention.
For me that means cup-and-core bullets are OK for my hand and lever guns. And for slow, heavy bullets from my bolts, like the 225g SST @ 2707fps from my 22" barreled .338WM. Other than that I prefer more solidly constructed bullets - bonded, mono, partitioned and hybrid designs. I did take a doe antelope several years back with a 95g SST from a .243 Win because I hadn't had time to work up any other load for that rifle and that load was super accurate. First time I'd used a cup-and-core to take game with a bolt rifle since my first back in the mid 1980's a spike bull elk where a cup-and-core lost over 50% of its weight after hitting a single rib.
While most bullets will work most of the time, I haven't has a premium bullets fail me in the 39 years I've been using them. That includes 20+ years with the Speer Grand Slam exclusively, Barnes MRX/TTSX/LRX, Nosler AB/ABLR, Swift Scirocco II/A-Frame and North Fork SS/SS-HP/FP.
(Back)ordered some Federal Premium 155g Terminal Ascent bullets for my 7mm RM yesterday and plan to have a load ready to go for elk season this fall. This is very similar to the North Fork SS and SS-HP I've used for years but with a tip, fewer grooves and higher B.C. (.586)