With a green field installation 10gbps network (no legacy equipment to support), why would one select one physical medium over the other? If left to impulse, I'd probably go with fiber optics over twisted pair because it is new and exciting. (Sparkly Pony!) But really, this should be a rational, logical decision.
I've very much interested in the "why" behind answers. E.g.: "Fiber performance can be degraded when placed near Kryptonite", "TP is 1000 times cheaper" etc.
(Background: I ask because I have a need to upgrade our Internet web/streaming servers network infrastructure at the data center.)
If you're using copper, your cable runs will be limited. (15m for twin-ax, 55m for STP/UTP). Also, bear in mind that you will need Cat6 if you go with the STP/UTP option. (Cat6a will allow you to run 10G/copper at distances of 100m).
The other thing you should look into is the relative cost of hardware. Most 10G fiber line cards are modular, with the optics being separate. This increases your initial outlay, but reduces replacement costs as generally optics fail at a much higher rate than line cards. I don't know if there are modular copper cards, and what the relative failure rates of transceivers vs. line cards are when using copper.
My bias would be fiber for all infrastructure (i.e. network-network) links. Having recently participated in a new DC build where we used Cat6 for all host connections, (even though we're only running at 1G), I'm not convinced by it. The cables are heavier and more difficult to run (less flex in them). The connectors, despite supposedly being the same spec as RJ45, seem to be slightly larger, which makes insertion/removal difficult.
Cost
twisted pair is much more susceptible for interferences
I recently read an interesting article (but it is german http://www.heise.de/netze/10-Gigabit-pro-Sekunde-ueber-Kupfer--/artikel/96475)
Most of the key issues have been mentioned - Fiber is easier to handle, weighs less, makes for a much neater environment and has better range (generally). As LapTop006 mentioned one consequence of this is that the port density on switches is generally higher for fiber, you'll find that many modular switches support a higher SFP+ port count than either CX4 (Twin-AX) or 10GBase-T (STP).
One other key difference is that at the moment 10GBase-T consumes more power per port than CX4 and in turn CX4 consumes more power than SFP+. That may not be of significance if you are only connecting up a few links but if you are building out a significant infrastructure then this may be something you need to pay attention to.
Use fibre with OM3 fibre, it works great, connects to every other 10Gb device and the actual fibre will support the forthcoming 40/50/100Gb standards too whilst copper won't.
How long are your cable runs? Fiber is always more expensive vs copper for any distance because of the infrastructure, and because it always leads the copper vendors by a few years.
I would go with Fiber, there is the possibility that in the future we might hit a dead end in how much speed can be had from copper. I mean twisted pair is as old as the telephone, now sure that means that it has had plenty of time to mature, but there exists the possibility of multiple colors running on the same fiber.
At this point the only copper 10Gbit switch with any density I've seen is Extreme's Summit X650, which they position as for intra-rack.
My general suggestion would be buy XFP/SFP+ gear and when running intra-rack save money by using the XFP-XFP (or XFP-SFP+ etc) cables available as one cable is often only 20% more then a single optic module.
If you're only just breaking gig-E then running pairs using LACP might be better for the redundency, as well as giving some time for 10Gig to hit decent densities.