Criticism: The Bible is archaeologically verifiable, so that means it's true without question. The Book of Mormon isn't archaeologically verifiable, so that means it's false.
Response: Read The Book of Mormon, The Doctrine and Covenants, and the Archaeology Question which illustrates and summarizes the fallacy of archaeological verification = theological verification arguments. The first comment at the end is a good one as well as the huge number of archaeology and evidence-of-authenticity articles linked in the footnotes.
Neither the Bible or the Book of Mormon have ever claimed to be primarily texts that can be physically verifiable by physical evidences. Both have the cause of converting people to the Gospel, not proving or disproving this or that archeaological or anthropological theory.
The fact that historical places of the Bible have been more adequately preserved while the Book of Mormon's have not is not evidence that the Book of Mormon is false. Lots of civilizations and their records have been lost to history. I'm sure there are plenty of subcultures in, say, Mongolia or China or Indonesia that we'll never know about because of the tendency of time and human activity to erase those evidences.
Central America is quite well regarded by archaeologists as a place where evidence of past civilizations is in rapid decay because of three factors: 1) climate (jungle rot being a key result), 2) foliage (huge trees with enormous root systems that overtake and pulverize mounds of rock placed by humans), and 3) human activity (later cultures overtaking and erasing the history of earlier cultures).
Here are some well-known examples of these three factors:
- Anything carbon-based or organic (i.e. that isn't rock) will either disintegrate in a few months to a few years, or it will grow. With the exception of gold, this is true of metal as well. Iron or copper implements will simply cease to exist in a couple hundred years due to high humidity, heavy rain, and acidic soils. The iron and copper weapons that were preserved in Mesoamerica were the extreme exceptions or were found in more arid areas.
- Guatemalans erect high fences by simply cutting the limb off of a tree, sticking the newly cut ends of the limbs into the highly fertile ground, and then waiting a year. That's how quickly foliage can grow there. Huge rainforest trees have massive root systems that hold the soil together, but also displace any solid objects in their path of growth.
- Pyramids built by earlier Mayan and pre-Mayan inhabitants were "repurposed" and built upon to create ever larger pyramids. In fact, a very familiar sounding name is given to some ruins in Belize that features this "stacking". The name the city's ancient inhabitants gave it was Lamanai (Lam'an'ain), which is identical to the Hebrew pronunciation for Laman (minus the suffix). We have only uncovered a few of these but there are many more out there we've not yet explored. In each one we've explored, we've been astonished at the amount of knowledge about preveious cultures through inscriptions and other evidences hidden in the layers.
The conditions under which the Nephites were exterminated in 420 A.D., with Lamanites spitefully and simultaneously erasing every part of Nephite culture and history, then what is the likelihood that we would find a remnant of their culture nearly 1600 years later? Don't forget also that zealous Spanish missionaries destroyed all but four Mayan codices. We're lucky to have what we have about ancient Mayans and their evidences more closely align with the decline of the Lamanites after the Nephite genocide.