To begin with, the sentence above has no (my) at all. It says (an expensive city) only.
However, I'll try to explain the difference between your 2 "sentences".
Logically and linguistically, the two phrases or sentences you've provided are completely different in meaning and usage, either in English or Arabic.
My expensive city: This is a phrase and not a complete sentence. The adjective here is attached to the noun as an attributive adjective. It is an adjective in use with the noun as one entity (and hence it is included after "my"). Typically in English, this is not to be considered a statement. Imagine saying to someone: Green wall - what's the point of this phrase? It does not state anything, nor provides any information. It is just a descriptive terminology for some wall which is green but we don't know anything about the situation. This is exactly the status of my expensive city.
My city is expensive: Here, we do have a full sentence. We have a subject (my city) and a predicate (expensive), all connected via a verb (is). In this instance, unlike the previous one, you are indeed stating some information to be delivered and not simply describing (my city). As an analogy in line, this is like saying the wall is green to someone. They now understand your point that you want to state and pin down the status of the wall that it is currently green. A subject, and a predicate.
Thus, the two statements cannot be used interchangeably. This is the case in English, and Arabic. In Arabic, however, the situation can be a bit delicate because all the difference relies on the presence of the definite article (AL).
- My expensive city: مدينتي الغالية (madínatí al-ğáliyah).
- My city is expensive: مدينتي غالية (madínatí ğáliyah).
Notice that the first phrase has (AL) attached to the adjective. This is because it is an attributive adjective. Attributive adjectives (which attach themselves to the noun in English) must follow the noun they describe in number, gender, and definition. The word مدينتي (my city) is defined automatically by adding the possessive (my: ـي) and hence its attributive adjective must be defined as well: الغالية (and of course it is in feminine form because مدينة originally is a feminine word).
The second sentence, the adjective غالية is a predicate (which in English comes after the verb "to be", or "is" in this case). Predicates in Arabic "must" be indefinite (most of the time, there are few exceptions). Thus, we see the adjectives when in a predicate position, would follow the noun which for they are stating the condition for, in number and gender, but NOT in definition.
Hope this makes it clear now.
An expensive city = مدينة غالية
(The) City is expensive = المدينة غالية
Notice the role of the definite article (AL) in the sentence above.
It might be a long talk but I'll try to make it short:
In Arabic, nominal sentences (sentences starting with a noun) cannot start with indefinite noun; Meaning: you cannot say A city is expensive in Arabic.
On the other hand, we have adjectives. Adjectives in Arabic can be in either two statuses, like in English; Either attributive (e.g. small cat), where the adjective (in English) is attached to the noun as a descriptive term. Or, it can be predicative (e.g. the cat is small), where the adjective is not attached but it forms a full sentence and tells a fact.
In Arabic, the attributive adjective (as in a small cat) comes after the noun and resembles the noun that it describes in definition, number, and gender:
- a small cat: قطة صغيرة
- THE small cat: القطة الصغيرة
Notice how the adjective الصغيرة became defined with (AL) just like the noun القطة. This is beside resembling the noun in gender (feminine) and in number (singular). What is important here is to notice the definition of the adjective.
On the other hand, the predicative adjective in Arabic does NOT follow the noun in definition. Thus, while the noun at the beginning of the sentence has defined (and it must be so in nominal sentences), we find the adjective is not defined:
- The cat is small: القطة صغيرة
As can be seen, the adjective صغيرة followed the noun in gender and number, but NOT in definition; It has no (AL). Thus, we conclude that we have a full sentence formed of subject (the cat القطة) and a predicative (is small صغيرة).
Hope this helps.