Change completion key in TextMate?
From the same question asked on SO:

To remap the esc key you have to copy

/Applications/TextMate.app/Contents/Resources/KeyBindings.dict

to

~/Library/Application Support/TextMate/KeyBindings.dict

and then edit it, preferably using TextMate :) as Property List Editor messes up the codes. 

Look for nextCompletion and previousCompletion and replace their values with whatever suits your needs best. 

For example, you could replace \033 (code for esc) to ->|tab.