The 00-04 3.8 is WORLDS ahead of the '83 carb motor. Close to twice the HP, IIRC. That said, it isn't known for great fuel economy. 24 to 27 average, in a 00-04 Mustang (mine averages 25.8, 4R70W automatic). I can't complain though. 315,000 miles and counting every day. So far, nary a single engine problem aside from a leaky water pump and a serpentine belt, but the power steering pump is getting a little noisy and will probably get replaced soon.
Also keep in mind that somewhere around 2000, a change was made to make the 3.8 internally balanced.
Also bear in mind that where a 3.8 came out of, a 3.9 (almost the same identical engine) will fit (those were in late 2004 Mustangs like what I have), and even better a 4.2 truck engine will go in where a 3.8 came out of too. So you get more inches, more torque, and potentially more HP with the 4.2. Both the later model 3.8/3.9 and as well the 4.2 can be had cheap because nobody wants them (free in a lot of cases). They can also be built to make some power. I think about 300hp is the max with the factory heads, maybe a little more-and that's with porting. Either way you go, the swap is going to be intensive as nothing is the same between the 83 and 2000-newer 3.8's, other than maybe the engine mounts. There were, to my knowledge, about 10 different versions of the same Essex V6's throughout the years. Front wheel drive blocks are different than rear wheel drive blocks, so keep that in mind too.
Now an SC 3.8 would be kind of neat. Or even a newer SC 3.8 or SC 4.2 using maybe a Lightning blower. BUT....make sure to use a steel crank. Factory offset rod journal cast cranks aren't the strongest piece in the world.
Guy on another board called "snoopstang" did an SVO Nascar V6 with a turbo and it ran awesome. Might google it.