Based on some digging, I think this is the correct answer, but anyone with more authoritative knowledge can feel free to correct me.
You can take a look at the READMEs that NCBI include within the directory for the genomes: https://ftp.ncbi.nlm.nih.gov/genomes/refseq/bacteria/Escherichia_coli/README.txt
From the text:
*_protein.faa.gz file
FASTA format sequences of the accessioned protein products annotated on
the genome assembly. The FASTA title is formatted as sequence
accession.version plus description.
*_translated_cds.faa.gz
FASTA sequences of individual CDS features annotated on the genomic
records, conceptually translated into protein sequence. The sequence
corresponds to the translation of the nucleotide sequence provided in the
*_cds_from_genomic.fna.gz file.
which relies on
*_cds_from_genomic.fna.gz
FASTA format of the nucleotide sequences corresponding to all CDS
features annotated on the assembly, based on the genome sequence. See
the "Description of files" section below for details of the file format.
The tl;dr appears to be that protein.faa
contains proteins which have accessions of their own in the protein database, whereas the CDS sequences and translated CDS sequence files are direct, simple, 'naive' in silico translations from the annotations on the genomes themselves.
To answer your original question: it depends what the analysis you intend to do is, but in 99% of cases I expect you'll want the proteins.faa
file.
You might have the stop codon represented by a star within the translated CDS if the translation comes from a gff file.
Open both file and check a common sequence to understand wath could differ between those two files
are you retrieving sequences from Genbank or RefSeq?