|There's more than one way to do things|
Actually, your problem doesn't have a simple solution. Two equal strings surely have the same numerical values, but what about two different strings? According to perlnumber these different strings all have the same numerical value: 1, 0x1, 01, 0b00000001
So, when $a eq $b says they are different, what would you do? I'll compare with == then! It's a simple or!. Gotcha! I am sorry, it's wrong: try to see what happens with ($a,$b) = qw(x y)...
What then? Well, when they are stringwise different, you have to choose again if you want to make a numerical comparison or not. You could check (by means of a regexp, for example) if $a and $b look like a number. If they don't, they are different and that's the end of the game; if they both are numbers you can (finally) proceed with ==
I had liked to find a better solution, but I think there isn't any.
The very nature of Perl to be like natural language--inconsistant and full of dwim and special cases--makes it impossible to know it all without simply memorizing the documentation (which is not complete or totally correct anyway).
In reply to Same number, different string [Re: my least favorite perl feature]