Is my DDR3 RAM really faster than my new DDR4?

So my GF just went out and bought her new build.
She went with skylake due to DDR4 and the newer CPU.

Got into a debate with the folks at microcenter because they kept telling me DDR4 RAM was faster than DDR3 but couldn't prove it. I've struggled to find any actual evidence that DDR4 is faster than DDR3... Can you help me out?

So my question is, does DDR4 have some time of bus increase or something that changes the equation at which we find its access time/effective speed?

Because I know that if the same speed and CAS of DDR2 and DDR3 were compared, that DDR3 would be faster. Does this also apply to DDR3 vs DDR4?

If 1866 CAS 9 DDR3 RAM was compared to 1866 CAS 9 DDR4 RAM would the speeds be equal? From what I've researched myself, the answer to that is yes.

If you use the same equation to find DDR3 RAM access time on DDR4... most common ddr3 sticks will beat common ddr4 sticks.

The RAM I have in my PC now is 1866 CAS 9 DDR3.
So to find that access time you take it's CAS divided by speed, and times that by 1k like so

9 / 933 = .00965 x 1000 = 9.65

Compared to my GFs new 2400 CAS 16 DDR4

16/1200 = .1333~ x 1000 = 13.33~

Lower access time is better, which means the DDR3 RAM is faster.
Now I realise we bought some value DDR4 RAM, but the DDR3 RAM that I have is also some value DDR3 RAM. But for the sake of the argument lets compare it to some faster more expensive DDR4 RAM.

CAS 14 2400mhz DDR4 corsair vengeance

14/1200 = .0116 x 100 = 11.66

...The DDR3 is still faster. Am I doing the equation wrong? Or am i missing something else entirely?





 
Solution
http://www.anandtech.com/show/8959/ddr4-haswell-e-scaling-review-2133-to-3200-with-gskill-corsair-adata-and-crucial/8 First link on a good search for DDR4 vs DDR3.

They compared 2133 CL11 DDR3 vs 2133 CL15 DDR4 and you see the results.

DDR4 has other advantages. It's new so you won't see huge benefits yet. It does allow for lower voltage, which is always good. Less heat, less power. It also allows for bigger densities. You can get a 128GB kit and a consumer level board. With DDR3, you can't do that with dumping 5x the money on a server board and ECC server RAM.
http://www.anandtech.com/show/8959/ddr4-haswell-e-scaling-review-2133-to-3200-with-gskill-corsair-adata-and-crucial/8 First link on a good search for DDR4 vs DDR3.

They compared 2133 CL11 DDR3 vs 2133 CL15 DDR4 and you see the results.

DDR4 has other advantages. It's new so you won't see huge benefits yet. It does allow for lower voltage, which is always good. Less heat, less power. It also allows for bigger densities. You can get a 128GB kit and a consumer level board. With DDR3, you can't do that with dumping 5x the money on a server board and ECC server RAM.
 
Solution