I have a profiled monitor yet I'm finding that I get prints that are MUCH closer to what my monitor renders when I let the printer (Epson 3880) handle the color management than when I let LR handle it. Yes, I've turned off "Printer Manages Color" in the printer controls. I've tried both perceptual and relative colormetric and noticed no real differences. Also tried printing from Photoshop which produced prints that were furthest from what was displayed on the monitor. I'm using Brilliant Exhibition Luster Paper and what I believe to be the correct profile (BrillLusterEP3880PK). Overall, the prints have a magenta cast when using the profile and appear more neutral when using "Printer Manages COlor."
Have you color calibrated your Monitor?
Does this happens with other Applications too?
Check if Printer drivers are up to date(download from manufacturer's website make sure its for 3880 not 3800)
Also If you have turned off color management in the printer, you have to use an ICC profile in LR that matches your printer and the paper you're using,Example
Actualy I believe the problem is in the profile provided by Brilliant. The best print by far (the closest to what it on the screen) was produced with Epson paper using the Epson provided profile. I know others love third party papers but staying within "the family" seems to have its benefits.
.. or you need something like SpyderPRINT ..