You wouldn´t say the engine is "faster," you would acknowlege it has more power....so your question is "how much more power does it have?"
Well, the first understanding is the GTX/R are turbocharged motors. Its the turbo that helps produce more power.
The GT 1.8L motor is spec´d at like 127bHP So its like right around 100 horse to the ground.
The GTX motor is basically the GT motor with a 3XXcc injector instead of the 2XXcc injector. Also, the GTX motors use bigger fuel pumps. So aside from the fuel system, the turbo...the biggest difference is the ECU. The ECU is designed to raise the fuel pressure in proportion to boost, and it retards the timing with boost too.
I know one of the things 323 GTX owners complain about with that ECU is it has a nasty habit of going lean at 10lbs of boost.
I think the GTX motor on stock boost is said to produce about 185 horse. Obviously uping the boost will increase power.
With all the peeps I´ve talked to and all the number crunching I´ve done, a 1.8L motor with a 3.35" bore and 3.27" stroke (I may have the two number´s mixed up, but do realize I´ve been bar hopping all night) using a turbo efficiency of 60% and an intercooler efficiency of 75% at 10lbs of boost can put about 215-225 HP to the ground.
But remember to push that much boost You´ll need either a GTX motor, or your GT motor with an upgraded fuel system.
The GTR is the only really different engine...I can´t seem to find alot of info on it, but I´m pretty sure the pistons themselves are different (dished I think), and the rings are better. I´ve heard the head gasket is better and stuff...hard to find info if you know what I mean. Anyhow, the GTR is like 210 horse on stock boost. Doesn´t really matter, your chances of even finding one are pretty much NILL.
Anyhow, how fast can you go? Now lets assume you´re going my route and doing a GTX setup on a GT motor. Lets assume nothing goes wrong and you run 12psi for one pass down the track. Well your scort is something like 2600lbs with fluids and 12psi is like 230-250 horse. Thats like a weight to power ratio of 10.5:1 ...9:1 would be AWESOME, 8:1 is like a supercar status. My guess is with 10.5:1 weight to power ratio and a perfect reaction time with lots of traction somewhere in the 14´s is possible.