Yes, Miechen would've outranked Ella though Ella was probably in a better position being close to NII when he was Tsarevich and then later when Nicholas married Alexandra. Miechen apparently wanted to gain the young Empress's confidence when Alix first arrived and be sort of a mentor but was rebuffed. With Ella's influence in that arena there could've been some bad feeling.
I don't have my Mager bio on Ella which probably talks about her early time as a leader of society but here's what Almedingen's bio has to say in regards to Miechen:
'Not all of the in-laws became her friends, but Elizabeth succeeding in avoiding friction even with the peevish and difficult Grand Duchess Michael and the formidable 'Miechen', wife of Grand Duke Vladimir, who, in spite of his frenzied Anglo-phobia, approved of the wife of a brother whom he held in anything but affection. The Emperor and his wife were great intimates, and Elizabeth grew very fond of their children, particularly of Nicholas..and of Xenia...'
re: Romanov women and war work
'Now the great star on the Petrograd firmament was Grand Duchess Vladimir, a consummate hostess, a woman of a great many gifts and as many ambitions....the handsome, imperious 'Miechen' had it all very much her own way. In justice be it said that she did more than organize balls and parties de plaisir . President of the Academy of Arts, she gave a helping hand to many a struggling artist. She prided herself on moving with the tiems, and poets, musicians, sculptors and painters could be met in her enormous crimson drawing-room. But Grand Duchess Vladimir possessed two unpleasing traits: contempt and jealousy. She despised her nephew, the Emperor, and considered his wife a nonentity. Herself a virtual stranger to Moscow, Grand Duchess Vladimir was jealous of Elizabeth's popularity there. Within the first few days of the war, 'Miechen' organized her own committee. She commanded great wealth and meant to spend much of it on war-work. It irked her to be excluded from those preliminary conferences at Tsarskoe and she is supposed to have said that 'dearest Ella surely had her hands full already what with her convent and all the paupers in Moscow'. [These comments reached her ears] but 'Elizabeth remained indifferent'. Gossip had long since lost its sting for her.'
'Quite a few members of the Romanov clan considered her [Ella] intransigeante. Grand Duchess Vladimir said that it might have been better if 'dearest Ella' had been entirely cloistered--such a chilly breath did she bring to the family gatherings, and why, Grand Duchess Vladimir would ask, appear at a wedding at all if you vanished immediately the service was over? Would a vocation be imperilled by a glass of champagne drunk to the bride's health and happiness.'