Battlefield uses enlightment, which is a radically different approach that has an 'offline' cost, and is less dynamic, also handles occlusions with more difficulty. But LPV is not the holy grail at all in that domain either. The advantage would be the very light cost. A better technique for geometric distant AO would be cone tracing but it costs too much memory and requires heavy shader model 5 code.
Voxel Cone tracing can be handled for newer hardware, and besides there's a lot of optimization room left. 3d compressed textures could help a lot with the memory problem. Speaking of voxel cone tracing, it can also handle direct lighting well in enough if you're using it already. Not only does it handle occlusion but you're also getting a full on image based lighting solution if you want.
The real problems with voxel cone tracing are other things, constant re-rasterization (though again, pre-computed voxels in a 3d texure could help a lot), thin geometry does not work well and how you'd handle things like grass and trees and stuff still needs to be worked out, not to mention the cone tracing itself is fairly expensive.
As for Battlefield, the original plan (As far as I know) was for dynamic GI. Unfortunately Enlighten's solution for dynamic stuff isn't terribly great, nor obviously nearly fast enough to run on the 360/PS3. Eventually they went down to PC only, and then just dropped it altogether.