Ele trabalha bastante. = He works a lot. Bastante here works as advérbio/adverb.
Ele trabalha o bastante. = He works enough. And here it work as substantivo/noun preceded by the article "o".
I have fun imagining a child coloring a square in an activities book. In the first case, the child painted not only the square but perhaps the whole page. In the second one, just the square was painted.
You'll have the same structure with different verbs, for example [ele]: fala (speaks), pensa (thinks), come (eats), etc.
You can think of them as synonyms, they both mean a great amount of something.
'Bastante' however comes from the verb 'bastar' (to suffice, be enough). So 'bastante' can give the idea of having this great amount of something that is so great and then enough.
You'll probably hear more often "Eu gosto muito de você." and "Já comemos bastante." "Eu gosto bastante de você." and "Já comemos muito" are also correct of course! Most of the times those sentences mean the same thing, but there can be a slight/subtle difference of meaning. I personally use "muito" more frequently.
I'd recommend this dictionary: http://www.priberam.pt/dlpo/