Besides the NAV, are there any other parameters which can be compared across different funds of the same category?

Besides Net Asset Value the following parameters should be considered while comparing the funds:
AVERAGE RETURNS An investor should look at the returns given by the fund over a period of time. Care should be taken to see whether all dividends and bonuses have been accounted for. The higher and more consistent the returns the better is the fund.
VOLATILITY In addition to the returns one should also look at the volatility of the returns given by the fund. Volatility is essentially the fluctuation of the returns about the mean return over a period of time. A fund giving consistent returns is better than a fund whose returns fluctuate a lot.
CORPUS SIZE A Large corpus is generally considered good because large funds have lower costs, as expenses are spread over large assets but at the same time a large corpus has some inefficiencies too. A large corpus may become unwieldy and thus difficult to manage.
PERFORMANCE VIS A VIS BENCHMARKS / OTHER SCHEMES An investor should not only look at the returns given by the scheme he has invested in but also compare it with benchmarks like the BSE Sensex, S & P Nifty, T-bill index etc depending on the asset class he has invested in. For a true picture it is advised that the returns should also be compared with the returns given by the other funds in the same category.
It is prudent to consider all the above-mentioned factors while comparing funds and not rely on any one of them in isolation.