Assuming the answer can't be C) Stainless Steel I would go with Aluminum.
The USDA specifically mandates (1) stainless steel 300:
"Milk contact surfaces shall be made of stainless steel of the 300
series, equally corrosion-resistant non-toxic metals or heat-resistant
Is the copper tinned? From what I can tell after reading some old sources (2) un-tinned copper will be corroded by milk. You have the advantage of a cool temperature lowering contamination risk (3), but many states following the FDA specifically removed the allowance of tinned copper (Sec. 22-201).
While the effects of life long dosing of Al are becoming more and more clearly tied to Alzheimer's (4), the effects build up over time. Copper has a tendency to be more acute (5) and pronounced (6, 7), and further it can tasted in low amounts and discolor the food (8). It can be said that water flows through Cu pipes, but soda is put in Al cans.
The research for this has been quite enjoyable, and led to things I didn't even think of. A alternative cleaning site has even recommended using milk to clean Cu pans.
Again so my final recommendation is to follow USDA guidelines and use stainless steel, but my second choice would be Aluminum.
(1) USDA. 2011, July. Milk for Manufacturing Purposes and its Production and Processing.
(2) US DOC. 1917, April. STRUCTURE OF THE COATING ON TINNED SHEET COPPER IN RELATION TO A SPECIFIC CASE OF CORROSION. Technologic Papers OF THE Bureau of Standards.
(3) COMMITTEE ON COPPER IN DRINKING WATER, NATIONAL RESEARCH COUNCIL. Copper in Drinking Water. NATIONAL ACADEMY PRESS. 2000.
(4) Walton, J.R. Aluminum Involvement in the Progression of Alzheimer's Disease. Journal of Alzheimer’s Disease 35 (2013) 7–43. DOI 10.3233/JAD-121909
(5) Reilly C. The dietary significance of adventitious iron, zinc, copper and lead in domestically prepared food. Food Addit Contam. 1985 Jul-Sep;2(3):209-15.
(6) Conor Reilly. Metal Contamination of Food:
Its Significance for Food Quality and Human Health. Pg 50. John Wiley & Sons, Apr 15, 2008
(8) ibid pg. 16
(7) Lee A. Price, et al. Chronic copper toxicosis presenting as liver failure in an Australian child. Pathology. 1996, Vol. 28, No. 4 , Pages 316-320 (doi:10.1080/00313029600169264)