Great disucssion.
I'm a big vodka martini fan (I call it a martini, not a vodka martini, but I recognize the historical difference). In my opinion it's all about what you like. If you like gin martinis, fine drink them. If you like vodka martinis fine drink them. In my experience, in modern bartending/cocktailing a "martini" is not recognized as being made with either gin or vodka, but what the drinker prefers.
Personally, if I wanted a gin martini I'd just go try to eat the pine tree in my backyard for the same flavor.
I kid, I kid. Kind of. If I'm drinking gin, is T #10, since that's the vodka-drinkers gin anyway. Sa[[hire has its moments, but I'm just not a giant juniper fan at the end of the day.
My preference: vodka martini. dry, up. with blue cheese stuffed olives. Amazing if made right. (I use M&R dry vermouth).
In terms of Vodka I'd use for it: Valentine's (local Detroit distillery and amazing), Ciroc (although by some standards not a vodka since made from grapes, but it was good even before Puff Daddy started advertising for it), Belvedere, Goose, etc. Those tend to be my selections, for value I'd go Ketel One or Smirnoff depending on what I'm looking to spend.
Funny how passionate people get about this in what is right/wrong. To each their own, I'm not about telling someone what is right/wrong.
I've become a big fan of what Valentine's calls a "fresh press" - not a martini, but vodka over ice with half an orange squeezed in it. That's it. It gives you a nice citrus flavor, but not nearly as overwhelming as a screwdriver and really brings out the great vodka flavor. It's a fun change (and I serve it in a rocks glass, not up), but it's of a similar vein of the martini idea of giving you good flavor of the alcohol and not the mixer.
Cheers.
