D'oh !!,
Sometimes I can miss the obvious.
I have posted that fallacy several times (read that as "many") where I have had one train of thought about it.
I have now tried this from iChat 5.0.3 in Snow Leopard to my iMac running El Capitan.
Sending from the iChat 5 machine eventually tells me it has failed due to an issue with the "AIM Proxy".
The File Transfer window on that computer continues to say it is waiting for a response from the other Buddy (my iMac)
The iMac never sees an Invite to accept a file and nothing appears in the chat window.
I then used the Bonjour Chat.
I text'd first and then sent from the iChat 5 machine again.
this was immediately marked as failed in the File transfer window on that machine and the Text Chat window on the iMac (El Capitan) shows a white info icon which in turn shows you the File Transfer window which states it failed
Attempts to send in the other direction are also met with the same things.

I am now not sure if the El Capitan version's lack of Invite window or any indication in the chat window is the cause or whether it is generally Apple Apps through AIM.
I then checked the Snow Leopard Firewall and found that iChat was not specifically listed and I added it.
Then Sending from the iChat 5 machine did cause the Invite window to appear on the iMac but the send still showed as failed at both ends using Bonjour.
Sending through the AIM Account results in the same "Waiting for Buddy to accept" followed by the same AIM Proxy message after a wait.
Nothing appears on the iMac end.
Nothing has changed in iChat 5.0.3 for years.
I checked the iMac's Firewall and it lists both IMAgent and Messages as I would expect.
Attempting Folder-ised items failed from the iMac over Bonjour, and in the reverse from the iChat 5 machine
Sending folder-ised items from the iChat 5 machine worked over AIM.
Zipped files seems to work both ways.
I am now more confused than before.
It is looking like a change to accepting pics-in-chats that show In-line has been stopped in the EL Capitan version.
However I will did deeper.

9:25 pm Tuesday; February 9, 2016
iMac 2.5Ghz i5 2011 (Mavericks 10.9)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
Couple of iPhones and an iPad