NSE has more liquidity and quality of companies listed is generally better (not talking about the blue chips or good mid/small caps). It's easier to get listed on BSE compared to NSE since NSE has a more stringent criteria for getting listed.
If you're interested in a specific stock which isn't listed on NSE then you anyway don't have a choice, however as a rule of thumb, I trade on NSE. NSE/NIFTY 500 is a good universe to pick stocks from if you're into trading (intraday or short term) since volumes are good and you don't need to worry too much about operators controlled stocks. You can additionally use daily average volume as a criteria to filter liquid stocks within NIFTY 500.
Hope this helps.Written Dec 02, 2020