There is a large diversity in the CIV broad absorption line (BAL) profile among BAL quasars (BALQs). We quantify this diversity by exploring the distribution of the CIV BAL properties, full width at half-maximum (FWHM), maximum depth of absorption and its velocity shift (v_md_), using the Sloan Digital Sky Survey DR7 quasar catalogue. We find the following: (i) Although the median CIV BAL profile in the quasar rest-frame becomes broader and shallower as the UV continuum slope ({alpha}UV at 1700-3000{AA}) gets bluer, the median individual profile in the absorber rest-frame remains identical, and is narrow (FWHM=3500km/s) and deep. Only 4 percent of BALs have FWHM>10000km/s. (ii) As the HeII emission equivalent width (EW) decreases, the distributions of FWHM and v_md_ extend to larger values, and the median maximum depth increases. These trends are consistent with theoretical models in which softer ionizing continua reduce overionization, and allow radiative acceleration of faster BAL outflows. (iii) As {alpha}_UV_ becomes bluer, the distribution of v_md_ extends to larger values. This trend may imply faster outflows at higher latitudes above the accretion disc plane. (iv) For non-BALQs, the CIV emission line decreases with decreasing HeII EW, and becomes more asymmetric and blueshifted. This suggests an increasing relative contribution of emission from the BAL outflow to the Civ emission line as the ionizing spectral energy distribution (SED) gets softer, which is consistent with the increasing fraction of BALQs as the ionizing SED gets softer.