"Jeg synes maden er brun" means that i have looked at the food and it seems brown.
"Jeg tror maden er brun" means that i have not looked and i am simply making a conjecture.
While "synes" can also be used about viewpoints and opinions , it only works in this way about things that are abstract or distant. When talking about things that are physically close to you, you would typically only use the word if you had taken a look.
I also think that 'jeg synes X er Y' can be translated as 'X seems Y to me'. So here, 'the food seems brown to me'. If it doesn't make sense to use the verb "seems" in English, then synes is not the right verb to use. I'd be interested to hear what other people think, but that's my understanding. That also makes sense given troelsvk's comment: the food can't seem brown to you if you haven't seen it.
for me, tror and synes are one of the major problems in danish. I understand tror as 'I believe this is the fact...' and synes as 'In my mind, according to my own belief, that makes ME think...'.
Some says synes is about an opinion. I never use that way of thinking cause it doesn't work for me (in my native language, many things including the weather are opinions, thus my spirit is currently not fit to this).