Scharnhorst and Gneisenau had strict orders not to engage any hvy secured convoy.
And please don't think about the old 11", as imho it is a misconception to think it was not useful enough.
The same as many think S was a BC, as it was not a BC, it was a fast BB with smaller main art.
It had very good modern ship and its armor was designed and applied with modern production technics.
Nowhere comparable with WWI.
Also maybe interesting, Germany decided for lower calibre as Uk most of the time, since the hvy Art of german warships was most time as effective as UK ones wich one higher calibre class.
Thats why the german designs had often still had 30cm whenUK had 34cm, or had34cm while UK had 38cm in WWI. Even with the Bismark class they were still staying with 38cm while common was already 40cm.
In S last Battle ~50 Torpedos were fired at S, and it had already cripled RADAR and was burning when in the bad weather also Duke of York opened fire.
DoY was a modern ship and not an old WWI type.
So it was not a "sitting duck" maybe but at least a blind duck pretty early in the fight and UK had a big position advantage. Not a fair fight for a comparison like we had in mind with one on one..
Look for comparison about the 12" of Alaska class:
The 28 cm SK C/34 had a lower shell weight as the Mark 8, but that is about also due the slightly higher calibre and type of ammunition of the Mark 8.
The Mark 8 heavy ammo was also 10 year later of design. And it is noetable that US was sure that the new ammunition type that was also used on the Iowas was capable enough to go head on head with Yamato if they had to.
Date for penetration power for 28 cm SK C/34:
http://www.navweaps.com/Weapons/WNGER_11-545_skc34.htm
http://en.wikipedia.org/wiki/28_cm_SK_C/34_naval_gun
This gun was also not used on Deutschland Class, that vessles used the older 11" gun(28 cm SK C/28).
Ramilles, wich was your first example had ~64mm -> 3inch..
While the 11" gun could penetrate up to 76mm.
And for the record, the upper deck armor of QE was also up to 45mm and the under deck armor was up to 76mm.
S had up to 105mm for its under deck armor..
But thats all statistics.
As you would need to take into account the placement of the armor, the angle and the armor type used etc..
If you look at the gun charakteristics, they are of course not as good as the modern more heavies of that time, but still hvy enough to inflict serious dmg.
Think about a "one on one", then S was also quite faster as R or even QE, it could decide when and if to engage, had a higher rate of fire(even higher as the Mark 8!) etc.
So its not a sure bet who will win.
And quite different as to think of a CA against a BC or even a BB. Wich would be silly in most situations if not in bad weather where the range would be limited etc..
Noteworthy is here that S got ist RADAR cripled by a CA shot in such circumstances. And UK commanders were of course quite often very good and bold in the usage of their ships.
Armor for Ramilles:
http://de.wikipedia.org/wiki/HMS_Ramillies_(07)
I've more data in books, but as I was writing that up between testing cool game features, I didn't found the time to look at them.
Cheers,
Chromos