He is wrong - watts are watts, and that's what the electricity company charge you for. A 50W 12V bulb needs as much power from the mains as a 50W 240V bulb. In fact, because of losses in the transformer, it needs slightly more power.
He is right - if you consider all of the running costs, not just electricity. In general 12V bulbs last longer than 240V ones, and in general they cost less to buy, although both types of bulb cover a spread of lifetimes and prices, and, of course, they overlap. And in any event, I suggest that if you are concerned about the actual differences you probably shouldn't be using halogen lighting at all.... Finally, there's the less obvious running cost of 12V systems - replacement transformers. The cheap electronic ones that you get with kits from the sheds are unreliable, and frequently fail. The proper design is 1 good quality transformer per lamp, but then this all costs more, which leads on to TCO.
He might be right, he might be wrong. When you get to TCO (Total Cost of Ownership), it's even less clear, because the capital cost of a 12V system is higher - you have to buy the transformers, and cables on the 12V side cost more than those in a mains system, as they need to be thicker. Obviously the effect on TCO depends on over what time you write those costs down.
Summary. It is difficult without knowing more about the comparative capital costs, and how long you each plan to keep the lights before changing them for something else to be sure which will be the cheaper system to run, and even then it'd only be a probability. I do know that analyses like these are like rearranging the deck chairs on the Titanic - both systems cost a lot to run, and the marginal differences are insignificant.
Personally I'd always go for mains - cheaper and easier to install, less to go wrong, easier to dim and better future-proofing; LED lamps are getting better all the time, and if you wanted those you could just swap them straight in, whereas your colleague would have to change his whole system.