Not really a direct Minecraft competitor.
Having downloaded it last night it's not the same game at all.
Yes they're both procedurally generated worlds with block based building. but they've as many differences as similarities. Whether they compete or not depends on what it is you like (or dislike) doing in Minecraft.
For MC players building purely cosmetic structures in creative mode this is definate alternative, especially for those who also use MCEdit in conjunction with the game itself.
For those more interested in the survival aspects of MC then LW doesn't (at least currently) seem to offer much. Although there are occasional mini-figs that you can punch there isn't really the same level of threat as in MC.Likewise there aren't really limits to resources - have as many basic bricks as you want. More complex models (flowers, oil wells, vehicles) you can have as many as you want too once you've found one (provided you have enough 'studs' to buy the first one - they're hardly in short supply).
For explorers LW might offer more. Rather than crafting things you need to find them in the world first (the exact thing, not a few multi-purpose general components), which means lots of travelling around. Time will tell if I'm right on this, it depends on how many things there are to find and how common they are.
For the more technical MC players who like redstone they're not going to find much of interest here. Building is (at least currently) limited to non-functional lego parts. Functional stuff like vehicles is found pre-built. I can see scope for this changing if the start including Technical Lego (aka Lego Technic) parts, but even that I'd expect to feel more like building contraptions in Besiege than MC.