Facts about the MP5:

It is the second most inaccurate gun in the game, after PM-9, only rivaled by the M60 and CM901.

MANY THANKS TO PSIJAKA FOR THE PICTURE SIMULATIONS OF THE RECOIL DATA!!

AK47 is there for reference as the second least accurate assault rifle after CM901.
Oh.
Here's the MP7 too for reference:

While M60 has grip, and PM9 the fastest rate of fire of all SMGs, CM901 and MP5 have no excuses what so ever as they are the LEAST accurate AR and SMG and they're also the assault rifle with the SLOWEST RATE OF FIRE and the SMG with the SECOND SLOWEST RATE OF FIRE...

MP5 was one of the more accurate weapons in the CoD4 beta, but firing at 800 RPM with decent accuracy (about the same as AK47), it overpowered everything in the beta.

So it got hit by the ugly-bat, with massive recoil, along with M4 which got heavy sway.

Because it was the only other SMG than AK74u that two hit kill on a decent range, it was arguably the best SMG in CoD4 (AK74u was better).
The P90 three hit killed, and was thus not a huge threath.

MP5's horrible recoil has followed it into MW2, Black Ops and now MW3.
Along the way, it's rate of fire has received a nerf, increasing recoil once again, and P90 has recieved higher damage, although at a lower rate of fire.
The PP90M1, PM-9 and MP7 also share the MP5's hits to kill on short range, making the MP5 completely outclassed.

Now let us go back to CoD4.
I will apply stopping power to all the weapons, obviously, because that was the hands down best perk apart from Juggernaut on M14, M60, P90 and Dragunov.

MP5: High recoil, 56 damage, 800 RPM
P90: Moderate-high recoil, 42 damage, 925 RPM
M4: Low recoil, 42 damage, 855 RPM
AK47: Medium-high recoil, 56 damage, 700 RPM

They were rather perfectly balanced, apart from the AK47 red dot and silencer inconsistencies.

Then MW2 came along.
MP5K: High recoil, 56 damage, 850 RPM
P90: Moderate-high recoil, 42 damage, 925 RPM
UMP: Moderate recoil, 56 damage 630 RPM
AK47: Moderate-high recoil, 56 damage, 666 RPM

Balance gets tossed up a bit because the SMGs with high damage enter AR territory.

Know that the UMP was deemed overpowered because it could 3 hit kill on long range without stopping power, with 35 minimum damage.
Even tough it got RAPED by AK47 at short range!
The analogy goes over to the MP7, which is an SMG that easily kills more effectively than UMP from MW2.

I'm skipping Black Ops and cutting to the chase:
Stopping power is out of MW3, and the stats look like this:

MP5: High recoil, 42 damage, 800 RPM
UMP: Moderate-high recoil, 49 damage, 750 RPM

Looking good so far...
PP90M1: Moderate-high recoil, 42 damage, 1000 RPM
P90: Moderate-high recoil, 42 damage, 850 RPM

WAIT JUST A F***ING SECOND NOW!!
WHAT WAS THAT??!?!?

MP5: High recoil, 42 damage, 800 RPM

PP90M1: Moderate-high recoil, 42 damage, 1000 RPM
P90: Moderate-high recoil, 42 damage, 850 RPM

Recoil:
(THANKS TO PSIJAKA for the perfectly representative recoil simulation!)

THAT is why I REFUSE to use ANY SMG in MW3.

MP5 = UMP < P90 ~= PM-9 < PP90M1 = MP7

Finally, the MP7's disgustingly absurd low recoil, compared to the G36C: