My educated guess, based on the limited evidence, is it's an early 1960s Competizione. I am basing that on the downtube decal (the word after "Bianchi" is more consistent with "Competizione" than it is with "Specialissima") and the componentry, especially the steel cottered crank vs. a Campy cotterless crank. The age estimate (early 1960s vs. mid 1960s) is based on the number of chrome stripes on the seat tube. Somewhere around 1963 or 1964 Bianchi wnt from two to five such stripes. The integrated head set certainly is consistent with my guestimate. It also appears to have the right brass colored head badge, although I can't be sure.

As for the tubing, if it is in fact a Competizione, it is probably built with a lesser grade tubing than the Columbus SL used in the Specialissima. Columbus didn't start using the terms "SL" or "SP" - and they are the same alloy, just differing thincknesses - for some years after the early 60s, but it was the same steel, metalurgically speaking. I have a 1961 Competizione frame recently repainted by Ed Litton (I rattle-can painted it in the 1970s when I was in high school), and he said my frame had seamed tubing, not the drawn Columbus SL/SP. One example is certainly not enough for saying for sure, but I would be surprised if my Competizione was a one-off.

My undertanding is that the "Competizione" was the lowest end frame made at the Reparto Corsa works and that is was meant to be the "entry level" racer. One then worked up to the Specialissima and another even higher level one.