Here's a basic comparison:

  Many small boxes
  
    Pros:
      - Cost. Small boxes cost less. Spend less or spend more as needed. If one dies, cheaper to replace.
      - Efficiency. Scaling *down* saves money when load is low. Can schedule specific loads to specific boxes.
      - Redundancy. Multiple VMS, OSes, network paths, etc. No single point of failure.
      - Zero-downtime. Rolling deployments, upgrades means changes with no user impact.
      - System bandwidth. More network links, cpus, kernels, disks, etc = more bandwidth, capacity.
      - Performance resilience. A heavily loaded app on one server doesn't affect others.
      - Immutability. "Pets" rather than "cattle" uses automation to reduce maintenance/instability.
      - Scalability. When you run out of resources, adding more is easy, zero impact.
    Cons:
      - Does not work with applications that require large memory/cpu.
      - Inefficient for apps that require shared filesystem access (as opposed to database).
      - Requires smarter architecture to reduce long tail of cross-host calls.
      - More transient network path failures, troubleshooting issues.
  
  One big box
  
    Pros:
      - Allows applications which require large memory/cpu.
      - More efficient for apps that share a filesystem.
      - Simpler architecture.
      - Fewer network path failures.
    Cons:
      - Large cost that you can't easily reduce as needed.
      - Waste (in unused resources) unless load is constant.
      - Single point of failure, for reliability and security.
      - Upgrades require reboots. App goes down; possibility the server might not boot up properly.
      - Single network, cpu, kernel, disks(s), etc become bottlenecks.
      - A single heavily-loaded process, excess interrupts, etc can bring down entire system performance.
      - Often treated as "pet" rather than "cattle"; creates more maintenance, instability.
      - Not scalable.

Big box VM host running several VMs, hardware starts to fail, brings the entire setup to its knees. That wouldn't happen if you had each VM running on its own physical hardware, unless the UPS/PDU died...