This is a pretty literal translation of your C file, that should perform exactly the same way (barring typos):

#! perl -slw
use strict;
use constant {
    COMP_FILE        => "list_comp.txt",
    COMP_TYPES_FILE => "list_comp_types.txt",
};

while( 1 ) {
    printf "svrmgr> ";
    chomp( my $command = <STDIN> );
    if( $command eq COMP_FILE ) {
        open my $in, '<', COMP_FILE 
            or printf("Error reading %s\n", COMP_FILE )
            and next;
        print while <$in>;
    }
    elsif( $command eq COMP_TYPES_FILE ) {
        open my $in, '<', COMP_TYPES_FILE 
            or printf("Error reading %s\n", COMP_TYPES_FILE )
            and next;
        print while <$in>;
    }
    else if( $command eq 'EXIT' ) {
        print "Disconnecting...\n";
        last;
    }
    else {
        print "Invalid command\n";
    }
}
exit 0;
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Easier to maintain?

(Also, just an aside. Are the blank lines in your C code an artifact of posting, or your preferred style?)