If you're trying to choose between Bitfinex and Binance then yes, go with the second option. However, It's still not recommended to store your coins in exchange unless you're planning to trade them soon, It's better to hold them in a wallet where you control the private keys.
True, but this can be difficult when trading all sorts of shitcoins. Both Binance and Bitfinex are adding fairly obscure coins at this point that I don't recognize, so I'm pretty sure I'm not downloading their core wallets either.
I'm pretty weary of Bitfinex after everything that's happened over the years. The ongoing Tether/banking FUD continues, which doesn't help. Binance seems like it's got some room to grow before it hits a wall with scaling limitations and it becomes the next Poloniex.