[EricH]

Vector attack! Assume you have a mecanum drive arranged this way:
(front)
/// \\\
\\\ /// roller pattern, 45-degree rollers.

Now, going forwards, the vectors will go:
\/
/\ with the arrows pointing towards the front. The sideways components cancel, producing:
^^
^^

Now, for sideways:
Vectors will go
.^...v
..\.../
../...\
v....^
(45 degree angles; v's are arrows)
The front-to-back cancel (obviously), so you should get the same speed sideways in theory. The problem is that when the robot is going forwards, the rollers "jam" better than when two wheels are going opposite directions.

Also, I have noticed this on several mecanum robots. Can it be compensated for? Sure. Is it easy to program a mecanum in the first place? No. I think the current controller is adequate for the job.

For some empirical evidence: My team once decided to try out mecanum drive. So we put one on a Kitbot. We tested it against an old 4WD robot. Speed forwards was about equal (once the mecanum was revved up a bit), even with relatively slick rollers. With the mecanum going sideways, though, the 4WD would win every time. Before the mecanum got to where we wanted it, the 4WD was there, every time.
(And, if you really want to make sure you translate sideways as fast as you go forwards, try an omni-drive.)