The most sensitive investigation for DCIS (Ductal carcinoma in situ) of the breast?
This is the controversial question some people are in favour of mammography and some are in favour of MRI. I have references for both.
"Mammography is the most sensitive and specific diagnostic tool available".
—The physiological basis of surgery 
"For DCIS, most studies have found that MRI is more sensitive than mammography for detecting multicentric disease".
—NIH DCIS
"Magnetic resonance mammography (MRI with breast coils) is the most sensitive technique for detection of breast cancel ; approaching 100% for invasive cancer and 80% for ductal carcinoma in situ (DCIS), but it has a high false positive rate (specificity is low)".       

To find the answer of this question. I went through various articles, books and sites. Recent studies show MRI is a more sensitive diagnostic tool but is less specific and costlier.
Following fact will also clear your doubt :
	
"The sensitivity of mammography for breast cancer is age dependent. The denser the breast, the less effective the method is for detecting early signs of breast cancer. Breast density tends to be higher in younger women and increased density obscures early signs of breast cancer : The sensitivity of mammography for breast cancer in women over 60 years of age approaches 95%, while mammography can be expected to detect less than 50% of breast cancer in women under 40 years age".        — Breast in women under 40 years.
The sensitivity of MRI is not very much affected by age.
Therefore, the overall sensitivity of MRI has to be greater than mammography.


According to me, the answer to this question is MRI. You are free to choose yours. Also, read the following information :

According to Author :

Most sensitive investigation for breast cancer in women > 60 years of age  →  Mammography.
Most sensitive investigation for breast cancer in women < 40 years of age  →  MRI.
Overall most sensitive investigation for breast cancer →  MRI.
Mammography
Ultrasound
MRI
PET scan