Yes they fit fine. They physically bolt up and work perfectly. But they will not be emissions legal.
The main difference is the 96 - 98 have 2 front EGR bungs and 1 rear bung on them where the 99 - 04 only have the single rear EGR bung.
I swapped a 96 Cobra engine into my 96 GT and deleted the front half of the EGR and used 99 - 04 BBK headers. I live in Fla and we have no emissions testing here so it was of no consequence.
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This is the engine I dropped in my car. If you look at the front of the exhaust manifolds you can see where the EGR tube comes out. There is one on the front of each manifold. 99 - 04 cars do not have this.
These are the 99 - 04 BBK headers I used. They just have the single rear EGR bung.
Here are the headers installed on the engine. The stock rear EGR tube bolts on perfectly.
96 - 98 long tubes on a 99 - 04 car can still be emissions legal if you plug off the front EGR connections. But 99 - 04 tubes would not be legal on 96 - 98 cars.
Hurst