There is a large diversity in the C IV broad absorption line (BAL) profile among BAL quasars (BALQs). We quantify this diversity by exploring the distribution of the C IV BAL properties, FWHM, maximum depth of absorption and its velocity shift ($v_{\rm md}$), using the SDSS DR7 quasar catalogue. We find the following: (i) Although the median C IV BAL profile in the quasar rest-frame becomes broader and shallower as the UV continuum slope ($\alpha_{\rm UV}$ at 1700-3000 A) gets bluer, the median individual profile in the absorber rest-frame remains identical, and is narrow (FWHM = 3500 km/s) and deep. Only 4 per cent of BALs have FWHM > 10,000 km/s. (ii) As the He II emission equivalent-width (EW) decreases, the distributions of FWHM and $v_{\rm md}$ 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 $\alpha_{\rm UV}$ becomes bluer, the distribution of $v_{\rm md}$ extends to larger values. This trend may imply faster outflows at higher latitudes above the accretion disc plane. (iv) For non-BALQs, the C IV emission line decreases with decreasing He II EW, and becomes more asymmetric and blueshifted. This suggests an increasing relative contribution of emission from the BAL outflow to the C IV 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.