Are you sure that Dialogic does not have some primitive protocol analyzer that will convert this for you?
The information you seek is somewhere in ITU-T Q.931 but it ain't going to be fun to manually translate it.
You really need a protocol analyzer to do this efficiently, but let me at least give a shot at decoding the message type.
The key is to understand that each pair of hex digits is a hex "octet" and represents an 8 bit binary word.
Octet 1 = Protocol Discriminator and should be 08 for call control signaling.
Octet 2 = always starts with 0000. The remaining digits indicate the length of the Information element.
Octet 3 First digit is 0 1 one and is used as a flag and should be ignored.
Octet 4 is the message type
Lets see the first 7th and 8th digits (fourth octet) of both of the IEs you give is 04 = 4 dec = 00000100
Q.931 defines this as "bearer capability". This is the type of call (voice, 3.1 kHz, or unrestricted digital information) and rate and related information.
The second Octet of the Bearer capability IE (e.g. digits 9 and 10) is the length of this IE and the third octet of the IE (11 and 12) are the transfer capability information.
So... digits 11 and 12 are 90 in the one message and 88 in the other case
90 hex = 144 decimal = 10010000
This is 3.1 kHz Audio (often used interchangeably with voice ). This is a call from a telephone. If you are a "modem" you probably would reject this call.
88 hex = 136 decimal = 10001000
This is is unrestricted digital information. This is a call from an ISDN digital device that is sending data. If you are a PBX you might reject this call (or limit access to DID numbers associate with ISDN data devices)
I am about 80% sure the above is right, but you need to get some sort of protocol analyzer. Took me over 30 minutes and I have some idea how it works and the correct standards to refer to.
I hope this helps
Good Luck.