Relative to 3.5, when prepped casters absolutely dominated Tier 1 thanks to their tremendous versatility, 5e casters gained: the equivalent of 3.5 spontaneous casting on top of the equivalent of 3.5 prepped casting, at-will cantrips including non-trivial at-will attacks, short-rest recovery of some spell slots, immunity to AoOs (not even any drawback to casting a save spell in melee), elimination of concentration checks for casting and maintaining spells, no loss of said concentration for being damaged/grappled/etc, the same spell DC for spells of all levels instead of the best DC only for the highest level spells, the ability to cast spells as rituals without using slots, and, for the wizard, even a better HD. In return, they lost damage scaling on spells by caster level (but gained scaling by slot without metamagic), got fewer slots overall, and had some of the most broken spells 'nerfed,' some of those with a concentration mechanic (that required no concentration check, can't be interrupted by damage, and only locks out other concentration spells, not all casting, unlike AD&D-era concentration).
That doesn't look like a net nerf, to me, and that's relative to the ed in which prepped casters were arguably at their most wildly overpowered. Relative to 4e, the power-up received by casters is much more profound - as is the slashing of options from martial classes - and, for that matter, the slashing of whole martial classes (there are arguably /no/ all-martial classes in 5e - all have at least one caster archetype - only a handful of non-caster archetypes). Even relative to AD&D, casters received a greater increase in options/power than martial classes, and a much greater easing of restrictions/limitations.
Anyone concluding 5e 'nerfed casters,' is probably focusing on one spell or mechanic that was wildly broken in some prior edition, that 5e has merely reigned in a bit.
