There is something about a martini,
A tingle remarkably pleasant,
A yellow, a mellow martini --
I wish that I had one at present.
There is something about a martini
When the dining and dancing begin,
And to tell you the truth,
It is not the vermouth:
I rather suspect it's the gin. -- Ogden Nash

In view of its being yellow, I suppose that that is the 19th-century-style martini, containing sweet & dry vermouth and orange bitters, such as I had before dinner this evening (no dancing, tho -- I was not born to inhabit a human body). In that company, IMO, the brand of gin scarcely matters.

When I lived in a commune in Virginia (1972-1981), I could not afford commercial gin, but there were plenty of junipers on the place, and their berries, crushed & infused in Everclear 180-proof vodka, produced a tincture a few drops of which would produce a ginlike flavor in any drink.

One might also (obSongs) recall Tom Lehrer:

One morning, in a fit of pique,
She drowned her father in the creek.
The water tasted bad for a week,
And we had to make do with gin.

By & large, I would say, the brand is irrelevant.