Can or should we perform feature counting with `bedtools intersect -c`?

[foolishbrat]

I have the following BAM file and a annotation file.
What I want to do is to calculate reads count in
I can do it with the following three methods.

• Method1 bedtools intersect
• Method2 bedtools multicov
• Method3 featureCounts

Below is the code

    #!/bin/bash
    INPUT_BAM=my_paired_end_alignment.bam
    ANNNOT_BED=peak_annot.bed
    ANNNOT_GTF=peak_annot.gtf
    
    # Temporary file
    ALIGNMENT_BED=my_paired_end_alignment.bed
    
    #-----------
    # Method 1
    #-----------
    FINAL_COUNT_METHOD1=output_method1.txt
    bedtools bamtobed -bedpe -i $INPUT_BAM > $ALIGNMENT_BED
    bedtools intersect -a $ANNOT_BED -b $ALIGNMENT_BED -c > $FINAL_COUNT_METHOD1
    
    #-----------
    # Method 2
    #-----------
    FINAL_COUNT_METHOD2=output_method2.txt
    bedtools multicov -bams $INPUT_BAM -bed $ANNOT_BED > $FINAL_COUNT_METHOD2
    
    #-----------
    # Method 3
    #-----------
    featureCounts  -a $ANNOT_GTF -o counts.txt $INPUT_BAM

The result given by Method1 is so different from Method2 (totally uncorrelated),
whereas Method2 is highly correlated with Method3.

My question is Method1 the right way to count feature? If not why?
Should we use Method2 or Method3 instead?

[GenoMax]

For reference cross-posted: https://www.biostars.org/p/270366/