/pat1/ && /pat2/
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/(?=.*?pat1)(?=.*?pat2)/s
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Note also that the OP didn't specify whether pat1 and pat2 may overlap. /pat1/ && /pat2/ has the potential to match more than /pat1.*pat2|pat2.*pat1/s. All of the presented solutions so far assume it's ok the patterns may overlap.

aren't equivalent in the first place.

Aside from the missing leading ^, what do you mean?

Granted, you need some extra code if you want to know what those captures are, but I don't see how they'll capture something different.

Or are you simply referring to the renumbering of the variables in backrefs?

Some examples:

    $_ = "foo bar foo";
    $pat1 = "(foo)";
    $pat2 = "(bar)";
    /$pat1/ && /$pat2/;          # Sets $1 (twice).
    /^(?=.*?$pat1)(?=.*?$pat2)/; # Sets $1 and $2.

    $pat1 = "(foo)";
    $pat2 = "(baz)";
    /$pat1/ && /$pat2/;          # Sets $1.
    /^(?=.*?$pat1)(?=.*?$pat2)/; # Doesn't set $1 or $2.

    $pat1 = "(foo)";
    $pat2 = "( )\\g{1}";
    /$pat1/ && /$pat2/;          # No match.
    /^(?=.*?$pat1)(?=.*?$pat2)/; # Match!
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As for the leading ^ - it only has a speed influence, and only if there's no match. But it can be a significant speed difference if the string is long, so it's better not to omit it.