The end result is the same, because the principles at work are the same. You won’t live what’s not in your heart to live.
The end result is NOT the same, in the least. First of all, we're talking the idea that "works alone" (c.f. the Old Covenant) will not gain Heaven for anyone, not whether some political scheme will be honored. Secondly, civil law is for EVERYONE--believers and unbelievers, notorious sinners and great Saints. No sane person thinks that civil laws should be abolished because "we're now under grace"; St. Paul certainly didn't think that (read Romans 13--so long as a law is just, those who resist that law are defying God), and neither should you.
Think about it: are you seriously proposing that NO ONE follows the law due to threat of punishment (i.e. the law isn't "in their hearts", but they fear punishment)? If so, I'll have to ask what planet you're on, because Earth is quite different. Plenty of people follow civil laws because they dread punishment if they're caught breaking it. Yes, of course, one whose heart is converted doesn't NEED the law, since he will have no desire to BREAK the law... but then again: that's the very person who doesn't MIND the law being there (especially for the sake of the unbelievers, backsliders, and other poor sinners who fall out of weakness). You won’t live what’s not in your heart to live.
That's a generalization which, when applied to the civic arena as a whole, isn't true. Plenty of people obey civil law for non-altruistic reasons... and removal of those laws would be INSANE.