As someone already said, Other M is closer to the traditional Metroids in gameplay. Prime is closer to Super in 'design'. But even then, its missing many of the standard equipment of Super (Speed Booster, Shinespark, Screw Attack, etc) not to mention it focuses a LOT more on forced exploration. And the first person view limits the combat compared to the virtual 360 degrees of sight and 8 degrees of attack. Also, you can't run in Prime.
One of the biggest arguments I always hear is that Prime is suppose to be a 'perfect transition of Super Metroid' because they both have areas you can explore outside the set path. But Prime does this WAY more than Super. As much as people want to claim Super had sequence breaking, it was limited to just areas you could wall jump or shinespark. The main game overall had a pretty set path governed by what items you could get. In Prime, you're practically forced to do 'sequence breaking' because the game has no set path and you have to constantly backtrack to previous areas you've been based on getting a new item. Good example is how you can go all the way to Pontera Drifts before getting the Super Missile or Charge Ball. Then have to go all the way back to Chozo Ruins and Tallon when you finally find it. Super never makes you go that far out of your way, except to get the Super Bomb.
As I've said before, Metroid Prime is more like playing Ocarina of Time with only a first person view and half the items turned off. It was a fun experiment, but its totally different than the traditional Metroid progression of gameplay.
Also, Other M took a lot from Prime. Though Sakamoto doesn't want to admit it, many of the first person aspects, and even some of the monster designs, were taken from Prime. Though the base gameplay mostly resembles a game like Fusion or Zero Mission.
Although I'm not sure I understand what details you feel were taken from Prime (not that there's anything wrong with that of course). I thought the first person part was a suggestion by team Ninja, and the monster design seemed pretty different to me...