Case-insensitive count duplicate line, remove duplicate by choose case with highest duplicate

I would use tolower() to make all the items lowercase. Then it is a matter of storing them in an array a[] and then printing the results:

$ awk '{a[tolower($0)]++} END {for (i in a) print i, a[i]}' file
xicolatada 6
hot chocolate 8

To have the output in comma-separated format, add -v OFS=,.

If that list of items is in a file named list.txt, you can do:

tr '[:upper:]' '[:lower:]' < list.txt | sort | uniq -c

...which will output:

8 hot chocolate
6 xicolatada

To pick the correct duplicate to output in the end you need to keep track of the global counts and unique (verbatim) counts; using awk:

#!/usr/bin/awk -f

{ l[tolower($0)]++; v[$0]++; }

END {
    OFS=", ";
    for (expr in l) {
        maxlc = 0;
        maxv = "";
        for (verb in v) {
            if (tolower(verb) == expr && v[verb] > maxlc) {
                maxlc = v[verb];
                maxv = verb;
            }
        }
        print maxv, l[expr];
    }
}

This counts all the unique lines in v, and their lowercase variants in l. l thus gives the counts of de-duplicated lines; for each of these, the script finds the matching occurrence in v with the highest count, and outputs that.

POSIXly:

<in dd conv=lcase|LC_ALL=C sort|uniq -c >out

...which prints...

8 hot chocolate
6 xicolatada

Or with GNU tools:

<in LC_ALL=C sort -f|uniq -ic >out

...which prints...

8 Hot Chocolate
6 XICOLATADA

You need a GNU uniq there - or, well, you need one which supports the case -insensitive option, anyhow. All sorts should do that with -f anyway.

This will give you your desired output

use List::Util qw(sum);

my %count;
while (<>) {
    chomp;
    $count{+lc}{$_}++; 
}

$,=", ";
$\="\n";

while (my ($key, $hash) = each %count) {
    my @labels = reverse 
                 map  { $_->[0] }
                 sort { $a->[1] <=> $b->[1] } 
                 map  { [ $_, $hash->{$_} ] } 
                 keys %$hash;
    my $sum = sum values %$hash;

    print $labels[0], $sum;
}

Then

$ perl count.pl data.txt 
Hot Chocolate, 8
Xicolatada, 6

The order of the output is indeterminate.