I love Toyota's, and I respect Jeeps. I happen to own/drive Land Rovers. I stick with them because I've invested time and effort in knowing about them, peripheral parts from one will fit on the next one etc. I could easily have the same relationship with another brand, but I'm kind of happy with my choice - and I'm a Brit so it fits.
Basing a decision on reliability alone is a strange one. I've owned many vehicles with reliability issues (including a brand new Porsche with multiple issues straight from the showroom), and while it's a contributory factor to the experience, I don't aspire to own something akin to plumbing - something that's easy to ignore unless it breaks.
And I don't know what Rover products would be comparable to a Tundra - or a Tacoma. They are pick-ups - only Defenders or old Series trucks come as a pick-up and I still wouldn't call them comparable. My wife had a Tacoma for a year, she liked it, I liked it, but she decided she didn't need a pick-up because the interior space was compromised (you know, because it was a pick-up)
I would hesitate spending only $2,000 on any Rover product (I'd hesitate spending that little on any vehicle) and expect it to be as reliable as a brand new Toyota. That really isn't a fair comparison. You might get lucky, but it'd be a very long shot or you'd spend a lot of time looking. Better to spend $15 to $20k on a well looked after vehicle (LR / Toyota / whatever) and modifying it your needs - slowly, over time. That way, you buy/attach the stuff you really want and need, and don't waste money buying crap you think you want (i.e. shiny new hi-lift jack and shovel attachment)
And I would set-aside budget / money to properly maintain and service your vehicle (either yourself, or pay the premium to have somebody else do it).
Any vehicle will break when used off-road, and then not maintained.
Other advice relevant to original question:
- There is much more after-market products and support for the Toyota products (Tacoma and FJ probably more than the Tundra) than for Land Rovers.
- Land Rovers and Range Rovers have developed significantly over the years. Ask for advice on particular models to understand what's desirable / undesirable. There are some wonderful gems and some woeful dogs, but this goes for any marque frankly
- Mainstream Land Rover dealerships won't like you. It's a real shame, but I never get a warm feeling when I go to one in a LR product that bears the scars of being used for what it was designed for. BUT, there are some awesome independent suppliers and garages (depending on your location) - check out Bill Davies at GBR in Salt Lake City
- If you're not a mechanic now, owning a Land Rover will make you one - but this is a good thing!
Good luck - exciting time to build a new vehicle!