Posting this in the NA forums will get you a NA weighted response.
I drove a 1.8L NA on my last car then swaped the engine out for a 1.8L turbo. Same engine, but factory turbo. The difference is staggering. You have a much more responsive throttle in the turbo, more pickup and just a better feel.
a 32 GTST is not a terribly quick car. But you will kick yourself if you get a 32 NA, it will be about the same speed or less as your pulsar due to added weight and added drivetrain loss, albeit with more traction. It wont handle as well as the pulsar did in stock form either.
The turbo has lag yes. But not much. At the end of the day the turbo version is the most common and most popular version because its got good power to weight. The NA version is very mild, im thinking of getting one for my daily driver because its a nice slow car with low fule consumption however it still looks the goods (for the record, I drive a 32 GTR, which is a 2.6L Twin Turbo AWD skyline)