1968 BARRACUDA WHEEL & TIRE OPTIONs !!!!

It's the tread width. Wider on a 60 series than a comparable 70 series.

I have factory 15x7 steelies, BBP on my 68. ALL factory 15x7 are 4-1/4 B.S. ALL. I have 215-60x15 tires and the passenger side clears by only 1/8". The driver side rubs when the wheel is turned but only in reverse. It is the extreme corner of the tire that hits the extreme lower corner of the fender. You can expect up to 1/2" difference from side to side per Mopar Performance.

Another thing that must be considered when talking tire clearance are the front brakes. My 73-75 A body front discs move the wheels outboard by something like 1/2" per side. This definitely affects the clearance when turning.

OP said he was considering 205-60x15 on the front with 15x7 and 4-1/4 B.S.. I would say that would work.
Also 15x8 with 4-1/4 BS and 245-60 tires on the rear will fit. Except I'd go 255.
This is why I went with 15x6 Pro Stars and 215x60x15 tires on the RMS front end with Wilwood brakes and the tires fit great and look great. I also have 275x60x15 Nitto Drag radials on 15x8 Pro stars on the rear that also work great. Stock wheel wells with a 8 3/4 and 002/003 SS springs. This is on my 68 Barracuda fast back.