You haven't actually answered the question other than to just state some perceived difference between "old" and "new". I want to hear all of the stories that you can create with the new... and how you might change the 5e tiefling to fit in your world. I couldn't care less about old vs new.
If you can't answer the question, that's fine... but ain't nobody got time for this. PHB hits next month, and I want your ideas.
Okay you want stories I got stories.
Sleea's great grandmother was said to be a descendant of the Evil War and Love Goddess Ianna, beautiful and terrible. But Sleea played little attention to that, figuring her family tree didn't matter after the rite changed Tiefling everywhere.
Then one day Sleea woke up with Ianna's mark burned onto her abdmen, with no idea how it got there, or why it was placed thiede. Did some spiteful Tiefling hating bigot put it there was has the dead Goddess Inanna returned like so many other gods back to life, to reclaim her childern from Asmodeaus.
Hecstern is the ugliest Tiefling you ever saw. As a young body his horns caught a fungus, that no magic has managed to cure, and the poisons produced by the fungus has cause his red skin to break out in hives and zits. Desiring to end his affliction, he has pledged to serve Sune as a Paladin in the hopes she will make him beautiful, but having a Paladin of Sune who is so ugly has enraged the local temple of Sune who has secretly put a price on this unsanctioned Paladin's head.
Lust is a stunning Paladin of Sharess from Memnon where her father is a mercinary, and her mother is a disgraced Fire Genasi noblewoman. Her training was given over to the local cult of Belial, but Lust rejected Belial, finding human scarfice vile and wasteful. Lust has six subling named after vices as well who followed her lead and rejected Infernal Worship. Lust is also close to her Fire Genasi mother. Her father is planning to have her killed, unbeknown to the rest of the family. Lust has little concsoius control of her tail which tend to have a mind of its own. Lust didn't have control over her Thaumaturgy either, drawing upon her connection to Asmodeaus unconsiously, but since becoming a Paladin of Sharess she's learned to draw on Sharess' power to full her innate Thaumaturgy instead. She still draws upon Asmodeaus power when she gets upswt enough to start cursing in Infernal, but it is not intentional.
Zeven is a Tiefling Rogue Assassin who practices his skill at Assassinations in the hopes of one day killing his father and his fellow rapists who attacked her mother one night in an explosion of antitiefling spite. Zeven is a zealous worshipper of Boar, and secretly believes he's a descendant of the Vengeful God, although he isn't, his ancestor is an Imp. When Zeven decides to kill, he surrounds his victim in darkness and strangles them with a cord.
Frandar is monk dedicated to develeping a unique martial arts fighting style that uses a Tieflings natural
attributes such as his tail, horns, and large canine teeth. Frandar was a refugee from Thay, his father, a human monk of Kossuth, raised him to fight and to honour his fiery nature. Frandar has never met his mother, but according to his father someday Frandar will return to Thay and free his Tiefling Mother from her Vampiric fate.