Based on everything I've read, Hayden Christensen is 6 feet even or 6'1". Prowse, at the time of the filming of the original Star Wars, was 6'6". Anakin Skywalker is roughly nineteen at the beginning of Episode 2 and roughly 24 by the end of Episode 3.
Human males can grow into their mid twenties, so the idea that Vader as he stands by the end of Episode 3 is taller than Anakin at the beginning of Episode 2 is perfectly reasonable. Both of my sons grew substantially after eighteen and into their early twenties.
Most importantly, the actor's height is not the character's height. Darth Vader was played by three different people in the original trilogy, only one of which was six and half feet tall. Most of his fighting was done by Bob Anderson in Empire Strikes Back and Return of the Jedi, who was only 6'1. Anderson wore lifts, but was probably not as tall as Prowse even so. The 6'10" soccer player in Invictus played by Matt Damon was not short because he was played by the sub-six foot Damon. Camera tricks were used throughout to make him appear taller.
Christensen, at 6'1, is also substantially taller than many of his castmates. He did not look short in either Episodes 2 or 3. He was visibly taller than Obiwan and Palpatine, more than the less than three inch height difference of the actors would suggest (Guinness, MacGregor, and McDiarmid are all 5'10). Christensen still towered over the 5'3" Portman, and scenes with them walking together certainly made him look very tall.
Finally, Skywalker's height on Wookiepedia is 1.88 meters (roughly 6'2), while Vader's is 2.02 meters, but Vader's height includes his helmet and boots, which he is never without, and 2.02 meters comes out to 6'6" roughly, making Vader in the helmet and boots as tall as Prowse without. That would put a fully grown Anakin with proportional limbs (Vader's limbs are proportional; his torso is that of a very large and tall man, which Prowse was, and he is always drawn as such, so the idea that they used longer limbs to make him so tall does not fit, as it would render a taller, narrower figure). Realistically, Vader without his helmet and boots would be about six three (an inch and a half for the boots and an inch and a half for the helmet, which sat atop an under-helmet/mask), so you're looking at only an inch difference at most.