Hendricks is infused with cucumber. Regardless of your sweet/dry preference, that flavor matters in every cocktail mentioned.
Hell...we aren't even talking about the differences between Genever, old tom, and London dry, let alone pot stills vs. modern stills, etc. All gin ain't created equal. They are as varied as "whiskey" when you get past the martini crowd.
Those who will talk about the topic, instead of talking about their other favorite spirits, are dicing about brand, rather than type. Which, I can understand, to some extent. If you are a Bombay vs. Beefeater person, that's one thing. They are both London drys.
But Hendricks, even as a dry, has a flavor component that throws it into a different class, IMO.
Tinman: if you just want a different London dry, my suggestion is Plymouth. It's a great staple at my bar.
Also, Grace gets -5 Internets for only being exposed to gins that have juniper in them, hence the "pine" problem. There are several styles that don't feature that at all. :P
TThog is also -5 Internets for being so myopic as to think that gin should be limited to quinine-infused beverages for the prevention of malaria. There is much more to the history of this spirit than just some Colonial mischief on the sub-continent.
For those that would rather just drink, explore and learn about why gin can be awesome: google is your friend on: The Pegu Club Cocktail, Corpse Reviver #2, and the Negroni.