They both cause the character to lose their Defense for the turn.
Can they be used together though?
The first edition core book does not explicitly state that you cannot lose your Defense more than once. The text of the Merit in question (Fighting Style: Boxing) does say that, if you have used your Defense already this round, you cannot use that technique. Dropping Defense for an All-Out Attack could be ruled as using Defense. Additionally, pg. 112 of Armory Reloaded (a supplement book) specifically prevent a character from losing their Defense more than once:
Furthermore, a character cannot give up his Defense twice in the same turn. If a Fighting Style Merit includes the drawback that the character’s Defense drops to zero, the character may not enhance that action with a supplemental style Merit that also negates Defense (nor can the character go All-Out).
Per the GMC update and second edition, you can only lose your Defense once, meaning you have to choose one or the other. This is specifically stated at the start of the Merits section.