As you likely know, Jutland was the first and really only major fleet action between large fleets of modern battlecruisers and battleships (before anyone says Tsushima, the battleships involved in that action were all pre-dreadnought). Because of this distinction, there was little opportunity prior to the war to develop procedures to deal with the problems that arose during such major actions. This list is probably something you have seen before or at least something like it and I know it is from Wikipedia but it is comprehensive and well sourced. I'll refer to it from here on out.

You'll see that the heaviest losses were suffered among crews of the Indefatigable, Queen Mary, Defence, Invincible, Black Prince and SMS Pommern. With the exception of the Black Prince, all of the listed ships suffered magazine detonations, catastrophic explosions that resulted in massive damage and very rapid sinkings that left almost no time for any crew that survived the detonation to evacuate, especially for anyone below deck. Additionally, such explosions likely cut power to the ship leaving the crews below deck in the dark as the ship sank, unable to find a route to evacuate.

While we know that the magazine detonations occurred due to the penetration of shell fire, the exact reason why those penetrations caused the magazine detonations aren't know. It is widely agreed that the failure to close the flash doors that were meant to prevent shell detonations from reaching the magazines were not closed on the British battlecruisers. Support for this comes from the testimony of a Gunnery Officer who served on HMS Lion who stated:

“…an enemy shell of large caliber…hit the turret and detonated inside the gun house, putting the turret out of action and causing, with the cordite fire that resulted from it, about sixty deaths…The Officer of the Turret, though himself severely wounded, realized that his turret was out of action and on fire, and also that the fire might reach the magazine. He accordingly passed his orders by the direct voice-pipe down to the handling-room below, to close the magazine doors and open the magazine flood valves. This order was promptly carried out, and did in fact prevent the flash from the cordite charges reaching the magazines, and so the ship from being blown up.”

That particular action likely saved the Lion from sharing the fate of Indefatigable and Invincible. A post-Jutland investigation made a similar determination. Admiral Beatty, the commander of the Battlecruiser squadron of which the Lion was the flagship, wrote “Undoubtedly [the] loss of Invincible was due to magazine doors being left open…I have given orders to battle-cruisers that magazine doors are to be kept closed on one clip….” From this it is easy to surmise that Beatty felt that it wasn't a matter of the flash doors being unsuitable but rather that they were not being used as they were intended to be, probably because keeping them open allowed for the faster supply of shells and charges from the magazine to the handling room and the turret above.

Admiral Jellicoe, the overall British fleet commander at Jutland, denied those claims and instead supported the theory that the battlecruisers were simply under armoured compared to their German counterparts. This was certainly true, German battlecruisers did possess thicker turret armour then British ships but experience both during Jutland and at Dogger Bank the year before showed that British shells did in fact penetrate the armour on German turrets. Furthermore, during Dogger Bank, the SMS Seydlitz suffered a penetration of one of its turrets by a shell fired by HMS Lion. The resulting explosion caused a fire which likely would have detonated the magazine had officers not flooded it. This lends credence to the argument that it was likely the improper following of procedure that resulted in the detonation of the magazines aboard the British battlecruisers.

I know this went off on a little bit of a tangent but I hope it does answer your question.

Source:

The First World War by John Keegan

Jutland: An Analysis of the Fighting by John Campbell

This well researched article by Marcus Magister

Just to add a bit to the answer you've already received, surviveability depended on a number of factors once a ship went down. The magazine explosion has already been mentioned, and all I'd add about that is this video of a battleship magazine explosion during WW2: https://www.youtube.com/watch?v=YdrISbwy_zI

Assuming you were able to avoid getting blown up in a magazine explosion (preferably by there not being one), the geographical location in which you were sunk made a huge difference. Most of the naval action in WW2 took place in Pacific, which tended to have warmer waters - you would still die of exposure, but surviveability in the water was measured in days, which provides plenty of time for rescue. While there was some naval action in the Pacific and the Mediterranean in WW1, most of it was in the North Sea and the North Atlantic, where the water was often cold enough that surviveability was measured in minutes (this is what took out most of the Titanic passengers and crew - very few drowned).

Another factor was how long it took somebody to notice that you need rescue. Radio communications technology in WW2 was pretty good, so you could send a voice message in the clear saying that your ship is sinking fast, please send rescue. In WW1, however, it was still in its infancy, and to send a message meant sending it in Morse Code and hoping that atmospheric conditions wouldn't prevent it from being received. To make matters worse, the smoke from the stacks (these were mainly coal powered ships in WW1) was quite thick and heavy, so if you were farther back in a line of battle, it was quite possible for your ship to be sunk and for nobody to notice that it had happened until some time later - which happened at Jutland with Indefatigable.

Assuming that your ship sunk and was noticed to have done so, whether another ship picked you out of the water depended on whether it was safe for the rescue ship to do so. There are innumerable cases of a ship going down, but nearby ships speeding away because of a submarine contact (and this is what causes most of Bismarck's crew to die of exposure in WW2). Once convoys were implemented, it was much easier for rescues at sea to take place, as you could have one destroyer chasing the U-boat while another rescues people from the water, but prior to that in the North Atlantic and the Western Approaches (a problem almost entirely a WW1 issue, as the British implemented convoys immediately upon the start of WW2), the mere presence of a submarine could prevent timely rescue.

There is a very good and credible video on this subject here (it's just under an hour long): https://www.youtube.com/watch?v=rbX8rJMI9GM&t=2s

The short of it is, however, that during WW2 sinkings usually occurred under conditions that made rescue more feasible than they did in WW1.

EDIT: I would add that there are a number of good books covering this material - Castles of Steel by Robert K. Massie gives some very good coverage of the Great War between Britain and Germany at sea; Hunt the Bismarck, by Angus Konstam, provides a perfect example of a rescue curtailed by the presence of a U-Boat; and for basic surviveability, literature on the Titanic provides a pretty decent grounding (particularly On a Sea of Glass, by Bill Wormstedt, J. Kent Layton, and Tad Fitch; and Report into the Loss of the SS Titanic, by Samuel Halpern et al.).