I have no issues with Land Rover reliability, it all comes down to maintenance and quality of parts.
As with any vehicle, stay on top of it and it'll serve you well.
I built my Defender 130 up from a rolling (just) parts vehicle. Loads missing and loads needed to be done to get it on the road AND reliable. Some 30,000 miles later and I'm just starting to service stuff for the second time (apart from the normal services every few thousand miles).
I get my parts from a guy who runs his own LR parts and accessories business and has been in the LR trade for over 30 years, so he knows his stuff and won't sell rubbish unless you specify a certain supplier and even then, he'll argue the toss with you. Buy cheap, buy twice. If it needs to keep fluids in (engine parts/gaskets, brakes, steering, axle seals etc... etc..., or has any wear surfaces (brakes, clutch, etc..., buy genuine, or good, long term manufacturer (Bearmarch for example), otherwise, for "inanimate" parts, pretty much any supplier on the market should be OK. Do not buy anything hydraulic from Br**part, I've seen too many wheel cylinders, master cylinders etc.. etc... fail, sometime right out the box, or within a few miles - for some reason, the quality control on far Eastern supply chain isn't brilliant.
I may be slightly biased, but go for Defender over Disco 1. Most Disco 1s will be rotting quite badly around the rear end by now, unless it's been in a really dry location for most of it's life. Having said that, Defenders can rot too. But, if you can get a good Defender, it will only gain value as the years go by and as you build it into a capable overland truck. There is something to be said for them as an investment, as long as you can dig deep to start with. I paid £5,000 for mine just over two years ago, and yes, I've put a lot into it (don't really want to think about that for too long !!!), but it's worth around £15,000 or more now as an overland truck, and I probably haven't spent any more than I would have building something else, that wouldn't be worth as much. You'll never loose money on a Defender, except the cost of the build and servicing.
There's more room in a 110 than a Disco, and load capacity is better too.