Hi, I've got a 3456, a 3457 and a 3468 (not the 78). The 3456 has one fewer digit of resolution than the 3457, and doesn't measure frequency or current, but it's probably my favourite meter. It has an LED display which is really easy to see compared to the LCDs on the other two, and it seems to capture faster than the 3457 for a given NPLC and resolution. But it's also about 47 miles deep from front to back, so you need one hell of a bench to use it on. The 3457 is a much more sensible depth.
There are minor differences in the math functions too, but I never use these so that doesn't bother me.
Needless to say, all the meters ware bang on accurate (compared with each other!) when I bought them (and they still are).
I hardly ever use the 3468, but it's significantly smaller than the other two and can measure up to 3A (1.5A on the 3457). I love the 3456 because it's big, clunky, heavy and complex when you open the lid, and it has LEDs and big clunky switches on the front. But you'd probably be better off with a 3457 - it's smaller, has more functions, extra resolution and is better on paper in almost every respect. Don't bother with a 3478 if you can afford a 3457.