Updated: Aug 31, 2020
The most significant difference is in taste and aroma. The taste of cold brewed coffee is generally less acidic & less bitter than hot brewed coffee. It therefore also brings out more flavour notes in complex single origin bean varieties. This is so because cold brew method is able to extract less of the coffee oils from the coffee bean in the brew which impart the acidic and bitter characteristics to brewed coffee.
It has decidedly less aroma than hot brewed coffee. A hot brewed coffee by any method can fill up an entire room with its aroma - be it a french press, pour over or espresso. No such thing with cold brew. This has an indirect impact on our perception of the overall taste of the brew.
Second difference is the purported health benefits as opposed to hot brewed coffee, since acidity is about 60% less than hot brewed variants on average, many experts claim that this has certain health benefits, although nothing has been proven conclusively yet.
Last difference of significance is the time it takes to brew a cup. Cold brew coffee can take up to 24 hours for the ideal 20% extraction which tastes best.
The same 20% extraction can be achieved in hot brew methods in a matter of minutes, and in a matter of 30 seconds or so in case of espresso.