I would say the Quad/Studio is a little more authentic, but you're not missing much with the Triaxis.
Depends on what Metallica tones you want, too. For example, the Triaxis and IIC+ were both used on Load, Reload, and Garage Inc. I've seen someone absolutely nail the Load tone on a Triaxis in Lead 2 Green. You'd swear it the raw tracks from the Load sessions if you didn't know any better. Plus, James and Kirk have used the Triaxis in their live racks for quite a while, somewhere around 12-15 years, with it being James primary live tone for many of them.
So it all depends on what you want. If you just want a MOP type crunch and that's all you care about, a Studio/Quad would be your best bet. Probably the same if you're just playing at home and/or recording since you can tweak settings as you need. However, if you plan on playing live and/or need a variety of tones, say a couple different sparkling cleans, a MOP crunch, a Load crunch, a couple different lead tones, etc...then the Triaxis would probably be a better bet.