I choose based on which one performs the best out of my rifle at the range. If you ask 10 different guys you will probably get 10 different answers. So buy two or three different brands. They don't have to be expensive. Federal Fusion is very affordable and gets very positive reviews, but it was designed primarily for deer. For elk, you may go with the Nosler Partiions or Accubonds. I took a real nice buck up in Wisconsin last November with Federal Fusion 180 grain.
I chose the Federal Fusion based on the groups I was getting with it out of my rifle. Maybe your rifle likes Federal blue box or Remington Core Lokts better. Federal Premiums with Nosler Partion bullets are a good pick, but you pay a little more for those. Honestly, if you hit a deer or an elk in the sweet spot with any one of those brands, its going down. So find the one your rifle likes best and go with it.
I use 150 grain fmjbt for hunting season. Good for crows, groundhogs, rabbits, and squirrels. I only had one limp away after being shot. I chased after it and finished it off with a knife. It was kinda hairy for a while. I had the head mounted....