If you have a profiled monitor you experience that some CMS-aware aplications render the image to a monitor different from others.
no, not really. Only whitepoint adaption may differ in rare cases (in an early Firefox version for instance)...
The following applications use the perceptual rendering intent:
Mozilla Firefox
you can set the rendering intend in Firefox.
http://kb.mozillazine.org/Gfx.color_manage...endering_intentBut... in practice it doesn't make any difference if an application translates perceptual or colormetric to the monitor profile.
TRC matrix based profiles do not contain a table for perceptual RI and even LUT based monitor profiles do not contain a perceptual table (AFAIK).
As the profiles do not contain any information about perceptual RI and common CMM's don't do their own translations here the RI to a monitor profile is de facto always colormetric.
You'll see a difference with the above mentioned test profile (as it contains the respective tables) but you won't see a difference with a monitor profile.
You can verify that for instance in Capture One (Pro) where you can set the RI in the preferences.