Short answer: no, they do not produce the same antibodies/immune response.

Somatic Hypermutation is not the only thing here but is one reason for this. The other reason is: T cells are actived in response to antigen being presented on cells with a so called Major Histogompatibility Complex (MHC). The antigen is not presented as a whole but rather smaller parts of it (peptides) are presented on MHC. You inherit the genes for MHC from your parents and the type of MHC that you have determines which antigen peptides can be presented on your cells.

This means that people with different MHC present different parts of an antigen to T cells which results in T cells with different receptors being activated.

Some peptides seem to be more crucial/important for a defense against a pathogen. This also means that some people are better in defending themselves against some pathogens because they can present those peptides that are more important. However, there's no type of MHC that is overall better for defense agains all different types of pathogens.

There exist thousends of genes for MHC in the human population. The reason for this might be that having many different allels and thus MHC complexes in a population makes it very hard for any one pathogen to eliminate a whole population since there probably will always be a part of the population that can defend themselves very well agains the parhogen.

My background: I'm a bioinformatics student and have had several courses about Immunology.