Not sure if it is quicker, it will depend on volumes, but you could Benchmark using a hash and RE:

my $string = 'ALL CHANGE, THOSE GOING TO ASCOT';
my %hash;

while ($string =~ /([AGCT])/g) {
    $hash{$1}++
}

local $, = ' ';
print %hash,"\n";
[download]

By the way, don't use switch/case, it is buggy and deprecated. Use given/when instead.