When I connect the USB 2.0 drive I see this:

usb 1-4.3: new full speed USB device using ohci_hcd and address 5

so I know it's getting seen as USB 1.1. usb-devices shows that it really is USB 2.0 and connected to a USB 2.0 hub:

T:  Bus=01 Lev=01 Prnt=01 Port=03 Cnt=01 Dev#=  2 Spd=12  MxCh= 4
D:  Ver= 2.00 Cls=09(hub  ) Sub=00 Prot=00 MxPS=64 #Cfgs=  1
P:  Vendor=05e3 ProdID=0608 Rev=77.61
S:  Product=USB2.0 Hub
C:  #Ifs= 1 Cfg#= 1 Atr=e0 MxPwr=100mA
I:  If#= 0 Alt= 0 #EPs= 1 Cls=09(hub  ) Sub=00 Prot=00 Driver=hub

T:  Bus=01 Lev=02 Prnt=02 Port=01 Cnt=01 Dev#=  4 Spd=12  MxCh= 0
D:  Ver= 2.00 Cls=00(>ifc ) Sub=00 Prot=00 MxPS=64 #Cfgs=  1
P:  Vendor=13fd ProdID=1340 Rev=02.10
S:  Manufacturer=Generic 
S:  Product=External
C:  #Ifs= 1 Cfg#= 1 Atr=c0 MxPwr=2mA
I:  If#= 0 Alt= 0 #EPs= 2 Cls=08(stor.) Sub=06 Prot=50 Driver=usb-storage

It seems the problem is that root hub is:

T:  Bus=01 Lev=00 Prnt=00 Port=00 Cnt=00 Dev#=  1 Spd=12  MxCh=10
D:  Ver= 1.10 Cls=09(hub  ) Sub=00 Prot=00 MxPS=64 #Cfgs=  1
P:  Vendor=1d6b ProdID=0001 Rev=02.06
S:  Manufacturer=Linux 2.6.32-25-server ohci_hcd
S:  Product=OHCI Host Controller
S:  SerialNumber=0000:00:02.0
C:  #Ifs= 1 Cfg#= 1 Atr=e0 MxPwr=0mA
I:  If#= 0 Alt= 0 #EPs= 1 Cls=09(hub  ) Sub=00 Prot=00 Driver=hub

And there's no mention of ehci_hcd.

lsusb -t gives me:

    /:  Bus 01.Port 1: Dev 1, Class=root_hub, Driver=ohci_hcd/10p, 12M
    |__ Port 4: Dev 2, If 0, Class=hub, Driver=hub/4p, 12M
        |__ Port 2: Dev 4, If 0, Class=stor., Driver=usb-storage, 12M
        |__ Port 3: Dev 5, If 0, Class=stor., Driver=usb-storage, 12M
    |__ Port 6: Dev 3, If 0, Class=stor., Driver=usb-storage, 12M

It seems like I'm missing something which would allow the OS to see USB 2.0 devices. Can anyone point me in the right direction?

EDIT

Full lsusb -v output:

Bus 001 Device 005: ID 13fd:1340 Initio Corporation 
Device Descriptor:
  bLength                18
  bDescriptorType         1
  bcdUSB               2.00
  bDeviceClass            0 (Defined at Interface level)
  bDeviceSubClass         0 
  bDeviceProtocol         0 
  bMaxPacketSize0        64
  idVendor           0x13fd Initio Corporation
  idProduct          0x1340 
  bcdDevice            2.10
  iManufacturer           1 Generic 
  iProduct                2 External        
  iSerial                 3 57442D574341595930323337
  bNumConfigurations      1
  Configuration Descriptor:
    bLength                 9
    bDescriptorType         2
    wTotalLength           32
    bNumInterfaces          1
    bConfigurationValue     1
    iConfiguration          0 
    bmAttributes         0xc0
      Self Powered
    MaxPower                2mA
    Interface Descriptor:
      bLength                 9
      bDescriptorType         4
      bInterfaceNumber        0
      bAlternateSetting       0
      bNumEndpoints           2
      bInterfaceClass         8 Mass Storage
      bInterfaceSubClass      6 SCSI
      bInterfaceProtocol     80 Bulk (Zip)
      iInterface              0 
      Endpoint Descriptor:
        bLength                 7
        bDescriptorType         5
        bEndpointAddress     0x81  EP 1 IN
        bmAttributes            2
          Transfer Type            Bulk
          Synch Type               None
          Usage Type               Data
        wMaxPacketSize     0x0040  1x 64 bytes
        bInterval               0
      Endpoint Descriptor:
        bLength                 7
        bDescriptorType         5
        bEndpointAddress     0x02  EP 2 OUT
        bmAttributes            2
          Transfer Type            Bulk
          Synch Type               None
          Usage Type               Data
        wMaxPacketSize     0x0040  1x 64 bytes
        bInterval               0
Device Qualifier (for other device speed):
  bLength                10
  bDescriptorType         6
  bcdUSB               2.00
  bDeviceClass            0 (Defined at Interface level)
  bDeviceSubClass         0 
  bDeviceProtocol         0 
  bMaxPacketSize0        64
  bNumConfigurations      1
Device Status:     0x0001
  Self Powered

Bus 001 Device 002: ID 05e3:0608 Genesys Logic, Inc. USB-2.0 4-Port HUB
Device Descriptor:
  bLength                18
  bDescriptorType         1
  bcdUSB               2.00
  bDeviceClass            9 Hub
  bDeviceSubClass         0 Unused
  bDeviceProtocol         0 Full speed (or root) hub
  bMaxPacketSize0        64
  idVendor           0x05e3 Genesys Logic, Inc.
  idProduct          0x0608 USB-2.0 4-Port HUB
  bcdDevice           77.61
  iManufacturer           0 
  iProduct                1 USB2.0 Hub
  iSerial                 0 
  bNumConfigurations      1
  Configuration Descriptor:
    bLength                 9
    bDescriptorType         2
    wTotalLength           25
    bNumInterfaces          1
    bConfigurationValue     1
    iConfiguration          0 
    bmAttributes         0xe0
      Self Powered
      Remote Wakeup
    MaxPower              100mA
    Interface Descriptor:
      bLength                 9
      bDescriptorType         4
      bInterfaceNumber        0
      bAlternateSetting       0
      bNumEndpoints           1
      bInterfaceClass         9 Hub
      bInterfaceSubClass      0 Unused
      bInterfaceProtocol      0 Full speed (or root) hub
      iInterface              0 
      Endpoint Descriptor:
        bLength                 7
        bDescriptorType         5
        bEndpointAddress     0x81  EP 1 IN
        bmAttributes            3
          Transfer Type            Interrupt
          Synch Type               None
          Usage Type               Data
        wMaxPacketSize     0x0001  1x 1 bytes
        bInterval             255
Hub Descriptor:
  bLength               9
  bDescriptorType      41
  nNbrPorts             4
  wHubCharacteristic 0x00e0
    Ganged power switching
    Ganged overcurrent protection
    Port indicators
  bPwrOn2PwrGood       50 * 2 milli seconds
  bHubContrCurrent    100 milli Ampere
  DeviceRemovable    0x00
  PortPwrCtrlMask    0xff
 Hub Port Status:
   Port 1: 0000.0100 power
   Port 2: 0000.0103 power enable connect
   Port 3: 0000.0103 power enable connect
   Port 4: 0000.0100 power
Device Qualifier (for other device speed):
  bLength                10
  bDescriptorType         6
  bcdUSB               2.00
  bDeviceClass            9 Hub
  bDeviceSubClass         0 Unused
  bDeviceProtocol         1 Single TT
  bMaxPacketSize0        64
  bNumConfigurations      1
Device Status:     0x0001
  Self Powered

Bus 001 Device 001: ID 1d6b:0001 Linux Foundation 1.1 root hub
Device Descriptor:
  bLength                18
  bDescriptorType         1
  bcdUSB               1.10
  bDeviceClass            9 Hub
  bDeviceSubClass         0 Unused
  bDeviceProtocol         0 Full speed (or root) hub
  bMaxPacketSize0        64
  idVendor           0x1d6b Linux Foundation
  idProduct          0x0001 1.1 root hub
  bcdDevice            2.06
  iManufacturer           3 Linux 2.6.32-25-server ohci_hcd
  iProduct                2 OHCI Host Controller
  iSerial                 1 0000:00:02.0
  bNumConfigurations      1
  Configuration Descriptor:
    bLength                 9
    bDescriptorType         2
    wTotalLength           25
    bNumInterfaces          1
    bConfigurationValue     1
    iConfiguration          0 
    bmAttributes         0xe0
      Self Powered
      Remote Wakeup
    MaxPower                0mA
    Interface Descriptor:
      bLength                 9
      bDescriptorType         4
      bInterfaceNumber        0
      bAlternateSetting       0
      bNumEndpoints           1
      bInterfaceClass         9 Hub
      bInterfaceSubClass      0 Unused
      bInterfaceProtocol      0 Full speed (or root) hub
      iInterface              0 
      Endpoint Descriptor:
        bLength                 7
        bDescriptorType         5
        bEndpointAddress     0x81  EP 1 IN
        bmAttributes            3
          Transfer Type            Interrupt
          Synch Type               None
          Usage Type               Data
        wMaxPacketSize     0x0002  1x 2 bytes
        bInterval             255
Hub Descriptor:
  bLength              11
  bDescriptorType      41
  nNbrPorts            10
  wHubCharacteristic 0x0002
    No power switching (usb 1.0)
    Ganged overcurrent protection
  bPwrOn2PwrGood        1 * 2 milli seconds
  bHubContrCurrent      0 milli Ampere
  DeviceRemovable    0x00 0x00
  PortPwrCtrlMask    0xff 0xff
 Hub Port Status:
   Port 1: 0000.0100 power
   Port 2: 0000.0100 power
   Port 3: 0000.0100 power
   Port 4: 0000.0103 power enable connect
   Port 5: 0000.0100 power
   Port 6: 0000.0103 power enable connect
   Port 7: 0000.0100 power
   Port 8: 0000.0100 power
   Port 9: 0000.0100 power
   Port 10: 0000.0100 power
Device Status:     0x0003
  Self Powered
  Remote Wakeup Enabled