I know this is an older thread, but if it helps anyone, I went through this debate too with my 2005 LR3.
My main concern was I wanted to put a full size spare tire under the vehicle in the stock location, not have to get an expensive (or in my opinion, unsightly) rear spare tire bumper mount, or to have to put it on a roof rack or in the vehicle. Other concern was that it's important for me to tow often, and I personally like and use the detachable Land Rover hitch receiver that snaps in and out, so it was imperative I was able to get that part in and out without the spare tire getting in the way, and to be able to get the tire up or down easily even if the hitch receiver was still installed as well. If you have an aftermarket hitch, you might want to make sure it's not going to get in the way of the spare tire. I also didn't want to have to make any modifications to wheel wells or bumpers due to rubbing issues.
So with all that in mind, I definitely concluded that 265/65 is as big as you can get in there without modifications or having to air the spare down to some silly stupid low PSI to stuff it in there with your foot or a jack. I was able to get a brand new full size 265/65 K02 in the spare location, just a very tiny bit of friction where the tire met the hitch mount location, but with just a tiny bit of tire bead grease on the metal in the hitch area, it slid in easily (that's what she said). Mind you these were brand new tires, when my tires wear out more, it'll be even easier to get it in there and out, and once my tires get down to say 15% tread left, I'll probably just leave one of them in the spare location and stop rotating it with the others so I don't have to buy 5 tires every time and rotate all 5 each rotation cycle. As far as rubbing goes on the fronts, I get absolutely none unless I hit a driveway curb only when in the lowest access mode, which is a rarity I'm in that mode anyways, I have never once had any in the "middle" road or highest off-road height settings, though I do have a very generous 3 to 4 inch software lift with the GAP IID tool which I do recommend (both the tool and lifting up at least 2" minimum).
Another note to consider is if your air suspension fails, as these sometimes can do and as mine did, when my compressor went bye-bye, that with the 265/65, when the vehicle went down all the way to the bump stops, the vehicle still had just enough clearance (barely) to not rub with these size tires, thus not destroying your wheel wells. If you want to go bigger than this tire size, the only other way around this issue is to get the SYA bump spacer kit I've seen from proud Rhino. This gives the air suspension another couple inches so if you go to bump stops, you don't bottom out your wheel well on the tire. Also helps with hyperextension when you already run a lift. Anyways...
As far as vanity goes, I can assure you the 265/65 still look very boss, at least with my KO2s, and as far as performance, 265 vs 275 really isn't going to be any dramatic or limiting factor in any trail situation when you run into trouble.
Anyone considering the two sizes won't regret getting the 265/65 size. It's nice to be able to fit it into the spare tire well without modification or have to modify your bumpers or wheel well plastics, and still looks way better and performs way better than the stock tires.
Only "mods" I made for these larger tires was to take out the plastic shield that sits between the spare tire and exhaust pipes and to zip-tie the wiring cable in the front driver side wheel well so that the tire wouldn't rub into the wiring protective plastic tubing when turned hard left. Just zip tie the cable set a bit higher up the frame and you will make sure it never rubs.
And if you haven't already...get the GAP IID tool. It's saved my bacon in countless ways and was the very first purchase I made due to recommendations from previous LR3/4 owners. Should have came with the car that's how instrumental and important and useful it is.