We extend our previous analysis of cosmological supernova data (Padmanabhan & Choudhury 2003) to include three recent compilation of data sets. Our analysis ignores systematic effects in the data and concentrates on some key theoretical issues. The first data set consists of 194 points while the second discards some of the points from the first one because of large uncertainties and thus consists of 142 points. The third data set is obtained from the second by adding the latest 14 points observed through HST. A careful comparison of these different data sets help us to draw the following conclusions: (i) All the data sets strongly rule out non-accelerating models. Interestingly, the first and the second sets favour a closed universe; i.e., the probability P(Omega_{tot} > 1) \gtrsim 0.97. Hence these sets are in mild disagreement with the "concordance" flat model. However, this disagreement is reduced [P(Omega_{tot} > 1) \approx 0.9] for the third data set, which includes the points observed by HST around 1 < z < 1.6. (ii) When the first data set is divided into two separate subsets consisting of low (z < 0.34) and high (z > 0.34) redshift supernova, it turns out that these two subsets, individually, admit non-accelerating models. However, these models seem to be ruled out using only the low redshift data for the other two data sets, which have less uncertainties. (iii) It is quite difficult to measure the evolution of the dark energy equation of state w_X though its present value can be constrained quite well. The best-fit value seems to mildly favour a dark energy component with current equation of state w_X < -1, thus opening the possibility of existence of more exotic forms of matter. However, the data is still consistent with the the standard cosmological constant at 99% confidence level (abridged).