In the first approach you are creating multivalued columns:
Cliente | Bairros
1005 | 1,2,3,4,5,6,7,8,9,10,11,12 (ColunaArray)
What is the problem with this approach? In a nutshell, every time you need to find all customers in a particular neighborhood you will have to do a like search, that is, a generic search in the neighborhoods column, this can be much worse than having "multiple relationships", I speak in terms of performance and maintenance (manipulation) of the data.
I found a very interesting post about multivalued columns in databases: link
In the second approach, using a table for clients , one for neighborhoods and a third for maintaining many-to-many relationships > You remove this problem regarding multivalued columns. Benefits? You will have standard tables ( First Normal Form or 1FN ), and simplify the process of finding customers by neighborhoods.
First Normal Form (1FN) - This is considered a part of the
relationship definition in the basic relational model. Its definition provides
that all the attributes of a relation must have their defined values
on atomic or indivisible domains. In other words, the fields
of a table must not be composite or multivalued. See below
a figure that shows the normalization of a table that is not in the
1FN for two relations.
For more information on the normal forms: link
It is important to keep in mind that there may be special cases where multivalued columns are required, however, whenever possible it would be advisable to avoid using this approach.