My 3 year old son drinks lots of milk, about 8 bottles a day. What would you recommend almond milk or cow milk?

Cut back on the milk. Truly as a pediatrician I strongly recommend that he not drink so much milk. Too much milk consumption in toddlers is a huge risk factor for iron deficiency anemia - which can be quite severe. Your 3 yr old should not be taking a bottle at this age. He should be drinking from a cup, and his milk consumption should be around 4 cups per day max.
Bovine milk problems. Bovine milk is a simple and effective means of obtaining calcium in a toddlers diet, but it has some limitations. Bovine milk in excess will cause microscopic bleeding in the gut, leading to anemia. Limiting it to 16-24 oz/day can avoid the issue. Almond milk would avoid the anemia, but not end the problem of a poor diet. Kids drinking that much are to full to eat a balanced diet.
Less milk. This much milk can lead to iron deficiency anemia. If he has no issues with cow milk I would recommend 3 glasses of cow's milk a day.