Both are great lodges in the same area, the Mtn Pine Ridge. Both are well staffed and managed. BL is on a creek that is dammed for swimming. HVI has a pool and hot tub near the cottages and restaurant.
Both offer the same area trips (Caracol, Mtn Pine Ridge, Barton Creek Cave, etc).
BL is on a small property that is well landscaped and designed. HVI is on 7200 acres of pine and hardwood forest. They have 7 private waterfalls, 90 miles of hiking trails and a stocked lake.
I think the 2 bdrm villas at BL are amongst the nicest in the country. The cottages at HVI have fireplaces.
BL will offer a larger menu selection for lunch and dinner. HVI will only offer a few selections. HVI has 12 cottages and BL about 20 plus.
Both are great and you'll be pleased with either.