Tactically, Beatty was ice-cold in battle. Jellicoe was never robustly tested on that score.
No idea where you get this impression of Jellicoe's record? Beatty may have been cool under fire, but that was common amongst the British admirals - Sturdee at The Falklands, Jellicoe at Jutland, especially leading up to the critical deployment of the fleet. It would be interesting to see an account of an admiral that was not cool in action, as I cannot think of a single example?
The thirty minutes leading up to the deployment of the Grand Fleet were probably the most critical of the entire naval war, and Jellicoe had no information from Beatty allowing a decision to be made with any certainty. He never showed the slightest sign of panic, and the deployment was probably the most perfect in naval history - a minor miricle if you look at what was known and the time needed to deploy. The signal 'Equal Speed Charlie London' lacks the direct appeal of 'England expects...' but it was far more precise and ensured naval supremacy for the remained of the war.
The biggest criticism of Jellicoe was that he was cold and did not rise to the chance to chase (over torpedo attacks and mines, not to mention the two extra flotillas that would have been brought into action by such a move) the HSF as it fled the action. The criticism was unfair and cannot withstand detailed scrutiny. The Grand Fleet was unaware the High Seas Fleet had turned about due to the poor visibility, most ships considering the failing visibility had caused the loss of visible targets (Beatty could see nothing at this point and had no idea what was happening either), and to charge blindly into the mst could have risked everything on a gamble that the British did not have to take.
After the war the naval staff regularly 'gamed' this scenario, using the full details now available from the German records and Jellicoe attended almost all of these sessions (Beatty did not), and nobody ever managed to produce a better deployment, or to inflict a greater defeat no matter what tactics were tried in over a decade of trying!
There would seem to be a distinct problem in listing a single thing Beatty did that could not have been done by any other admiral, or indeed any offer of an excuse for the dreadful results achieved by Beatty during the war? If Jellicoe had been served by an officer of the quality Hipper was and not Beatty, there would have been no High Seas Fleet after the morning of June 1st 1916.