According to http://www.quadibloc.com/comp/cp0201.htm
The CDC 1604 used 48-bit floating point with 11 bits exponent and 36 bits mantissa. There was also a double precision format (which I believe was added later as an option) that simply adds an extra 48 bits of mantissa.
The CDC 6600 went up to 60 bits, 11 exponent, 48 mantissa. There does not seem to have been a double precision option.
I think it is worth noting that both computers came not only from the same company but the same designer, Seymour Cray. So the designer changed his mind, between those two machines, about the optimal floating-point size. (We are used to word size being mostly about the required size of addresses, but these computers were built primarily for fast floating-point arithmetic; the address sizes were separate and smaller.)
I can think of two reasons why he might've changed his mind:
Experience with the 1604 showed 48 bits was not always enough, so a double precision option had to be added. Cray took that experience into account when designing the 6600.
Maybe 48 bits was enough for the 1604, but was not enough for the 6600, which because of its greater performance would be used to perform longer chains of calculations, creating more opportunities for rounding error.
In other words, was the 48-bit 1604 a mistake, discovered to be such once it had been used in production for a while? Or was 48 bits the right choice for the 1604 but not for the more powerful successor?
Or was there another factor I'm not taking into account?