While vegetables offer a whole swath of vitamins and minerals, animal products (meat, eggs, and dairy) are the best sources of:
Choline, of which eggs are the highest animal source at approximately 200mg per yolk
Carnosine, which is commonly supplemented as the similar compound Beta-Alanine
Phosphatidylserine mostly in fatty fish, although legumes have a small content
The omega-3 fatty acids known as fish oil, comprising of EPA (Eicosapentaenoic Acid) and DHA (Docosahexaenoic Acid). Plant sources contain Alpha-Linoleic acid, an omega-3 fatty acid, which the body is not efficient at processing..
Vitamin B12, otherwise known as cobalamin (can also be found in rotten foods via bacterial production)
The above compounds are not vital nutrients to the body (except B12), but they seem to be more potent when supplemented to vegetarians.
For example, creatine supplementation is known to enhance cognition in the elderly (a state of cognitive decline) and vegetarians but not omnivores of normal cognitive capacity. Suggesting the vegetarian/vegan diet may be one of relative creatine deficiency (not absolute deficiency, as some creatine will be produced naturally).
Examine has noted that vegetarians may also be in a Carnitine deficient state as noted here, and how studies showing enhanced fat metabolisms in vegetarians with carnitine supplementation have falsely been extrapolated to all populations.
Some compounds, like Phytanic Acid, have notable serum (blood) differences when comparing vegans to omnivores.