There is quite a bit to be done with some controled randomness in shmups and if done right it doesn't need to hamper competitive play.
The game generates enemy waves and bullet patterns, not randomly, but not completely scripted either. You definitely don't play the same patterns each time and it is mostly about twitch skill. I haven't heard anyone complaining about that when playing for highscores.
You fight a single boss which evolves as you destroy it and as you die. The evolution of the boss is not quite random, but they are diverse enough that each player has a different experience and from what I remember people played for high scores since there is quite some strategy and execution involved in surviving for the longest time possible.
This one is quite cool. The game detects what attacks are killing the player and adapts itself to attack with more of the same. You can purposely kill yourself with easy to dodge attacks so the AI will attack you with easier patterns as you get farther into the game.