Bash, 94 86 bytes (saved eight bytes thanks to Digital Trauma)

p=equal;q=than;(($1>$2))&&p=greater&&[ ]||(($1<$2))&&p=less||q=to;echo $1 is $p $q $2

Test (on Linux):

echo 'p=equal;q=than;(($1>$2))&&p=greater&&[ ]||(($1<$2))&&p=less||q=to;echo $1 is $p $q $2' > cmp.sh
chmod +x cmp.sh
./cmp.sh 10 12
10 is less than 12

The use of [ ] after p=greater is to prevent || operator from being evaluated before = in the expression ...&&p=greater||(($1<$2))... (the operator precedence!).

The alternative would be using brackets around (($1>$2))&&p=greater and (($1<$2))&&p=less , but brackets make inner scope for variables, so p would be left unaltered.