In English, articles, demonstratives, and possessive determiners cannot co-occur in the same phrase, while any number of adjectives are typically allowed.
A biggreenEnglish book
* The his book (note however that Italian allows exactly this construction - il suo libro)
He is happy .2 * He is the.
Most determiners cannot occur alone in predicative complement position; most adjectives can.
happy, happier, happiest
(However in colloquial usage an English speaker might say [eg] "This is very much my house" for emphasis)
Most determiners are not gradable, while adjectives typically are.
Each likes something different.
* Big likes something different.
Some determiners have corresponding pronouns, while adjectives don't.
a big person / big people
many people / * many person
Adjectives can modify singular or plural nouns, while some determiners can only modify one or the other.
Adjectives are never obligatory, while determiners often are.