I thought this scene was a little stupid. The race was presented as a big struggle where scrappy Brian's skills behind the wheel and slick mods to the Supra allowed them to prevail. The F355 and especially the 348 were pretty unremarkable cars as Ferrari's go. A stock Supra could have have given one a run for it's money. If the movie Supra was all they implied, this shouldn't have been much of a challenge.
You can't say that the 355 isn't a fast car, anything that can beat it is pretty impressive. The Ferrari 550 wasn't miles quicker, and it would have been a bit far-fetched to put an F50 in this scene. What I think I this scene tried to illustrate was the difference between someone who was really into cars and had worked hard to modify a car into something really amazing, and some arrogant rich man who had just gone into a showroom and bought a fast exotic car without any real effort.
You might be right. I've always found it amusing though that the 348 came to market about the same time as a crop of truely remarkable performance cars like the 320 horse Supra Turbo, the gen 3 Mazda RX7, and the Mitsu 3000GT VR4 - cars with genuinely competitive performance for a quarter of the Ferrari's price. Car & Driver even ran a 348 against a GMC Syclone and found the Italian pretty easy to keep up with.