This is a replica site... and as such, the perspective you'll get here will obviously be slanted towards the virtues of a replica. Over on "the Registry" site, you'd probably get a different opinion.
With an original 356, you get authenticity and history- and everybody should be aware that there's no way to replicate either of them. I can equip my car to appear about 99% original, and even fake a bit of patena to make the car look "old", but nothing will ever change the fact that it was built a couple of years ago. The authenticity and history of an original is kind of cool, and worth (a lot of) money- but it won't bring more than about 5 minutes of enjoyment looking at the car, and none at all driving it.
A replica is simply more usable. I can drive my speedster to the store, and leave it in the parking lot without feeling like I've left a 4 ft tall pile of $100 bills sitting unattended on the parking lot. I can change the exhaust for a merged unit, install a fire suppression system, or any one of a hundred other things- and not have destroyed a piece of history. I can "drive it like I stole it", bash the sump on a speed bump, and not need to take out a second mortgage to fix it. I can install a monster 200 h/p engine and all the related stuff, and never worry that the numbers don't match any more.
There are guys who do this kind of cool stuff with original 356s. They own islands, and these cars are trifles to be played with. The Emorys do this all the time. Their cars start at way over $100K and go up really, really fast from there.
With either car (original or replica), even a heavily modified one, you're going to have to live with 50- 70 year old technology- these aren't modern cars, and they reward people with some mechanical skills going into the deal.
To sum it up- If what people think matters to you, I'd buy an original. If you are a "car guy", and want to work on and improve your car- I'd buy a replica. If you just want to get in and drive it, rain or shine- I'd buy a nice used Boxter.
It's really up to you. These cars require some compromise. If you aren't willing to make them, you probably aren't a good candidate for owning one.