That's it exactly, the focus moved away from stage design. Can we call it a subgenre? Maybe it's more like a lateral evolvement, a genre of its own it sure is I guess. And I'm not bashing those games, they're just not my thing.

I'd propose there's three subgenres for shmups, then: one's the Bullet Hell genre exemplified by Crimson Clover, where the focus is on learning bullet patterns; another is that of Overkill, where the main focus is on navigating the stage and its obstacles, with enemies only a secondary concern; and a third would be that of Raptor or Raiden, where the focus lies on neither stage nor bullets, but on learning enemy movement patterns instead.

And if we go with that classification... I like all three :D though I like the second type the least, even if Overkill was my "entry drug" into the genre: losing a life because I crashed into a wall or obstacle feels cheap and unfair in a way getting hit by a bullet or crashing into an enemy doesn't, even though rationally there's not much difference between one another. But YMMV of course.

I don't know about Raiden, but in Raptor there is also a bit of a puzzlesolving present. To get through some tight spots, you have to figure out what weapon to use and when precisely drop Megabombs.
Isn't Tyrian essentially Raptor with different "story"?

I always thought it played much smoother, different feel but maybe that's me.

Also Tyrian has more of a sense of humor with the christmas stuff and the carrot ship that fires bananas and oranges.

Never played Tyrian (fo' shame, I know), but I think upgrades are transversal to the issue of the primary danger; in Overkill for instance you had to kill the bigger enemies for their parts so you could upgrade your lasers, add drones or the likes, and in fact putting such enemies in tough spots was the game's way of luring you towards almost-inescapable walls, which were the real danger. Whereas in Raptor, since upgrades were bought between missions and you had to kill more ships to get money, it in turn became a way for the game to needle you into learning enemy patterns so you could maximize your kills-per-run.

Proper use of screen-clearing bombs is a key part of almost every shmup; it's key for surviving the worst patterns in Mushihimesama for instance, which is one of the most bullet-hellish bullet hells there is :D they're less useful in shmups like Overkill, but mostly because you can't bomb walls away so you'll still go *splat*.

There are some games, like some of the Touhou games, in which proper use of bombs is part of the strategy for getting a high score. In particular, when you bomb, you become temporarily invincible, and as a result, it becomes possible to go into otherwise unsafe spots and graze hundreds (or perhaps even thousands) of bullets, and in some Touhou games, the number of bullets you've grazed affects the amount of points that point items give you.

Also, note that dying in Touhou games will typically set your bombs to 3, I believe, so sometimes the high scoring strategy involves dying on purpose to get more bombs.

Here are a couple interesting cases regarding bombing in the Touhou series:

Mountain of Faith: In this game, bombing costs you one unit of power (instead of having a limited number of bombs). Normally, this would be a bad thing, but it happens that if you are playing as MarisaB, your power is at least 3 but less than 5, and you are not focused, your shots do a huge amount of damage. (Apparently, ZUN put the decimal place in the wrong spot, so your shots do 10 times the intended amount of damage.) Therefore, if you reach 4 power, you will actually do more damage if you bomb to reduce your power to 3.

Double Dealing Character: In this game, MarisaB's bomb will turn incoming bullets into power up items. It just so happens that, if you collect enough items in a short enough period of time, you will get a third of an extra life. Combine that with the fact that dying refills your bombs and you can actually come out ahead on resources. This strategy actually works best on Lunatic and Extra difficulties where there are more bullets to turn into power items. (I believe I have seen at least one video where the player died a double digit number of times and *still* one with max lives.)

Edit: Added "a third of" to make the post more accurate.

Tyrian & friends are a strange bunch. I mean, everybody already knows Tyrian's "euroshmup" designation I suppose, some think it is the best shmup ever, some the exact opposite -- for full disclosure I'm in the latter camp.

I played it to death back in the day, yet I find it difficult to group it together with Japanese-style shooters. It feels like a game in a completely different genre which happens to feature a spaceship on a scrolling background, but the similarities stop there. It is fun all right, but I can't shake the feeling that I am playing something more akin to a crane game where luck and trial-error trump everything else.

I enjoy shmups that are employing all of these features. It brings a variety in gameplay that challenges you in different ways throughout. Ikaruga is one stellar example for this.