If you want to try out homebrewing without investing much in terms of cost or taking up a lot of space and time, I would go with the Mr. Beer over The Beer Machine. My main issue with the Beer Machine, is that you never take the beer off of the used yeast bed. I don't have the machine, but it appears to me you ferment it and just set it in the fridge, and then dispense it straight from the keg. After about two to three weeks (one of those is spent fermenting), you are going to get off flavors from the yeast bed. It is also a pretty expensive little device. For $100 you can nearly get a full blown set up. The Mr. Beer is $39 and comes ready to go with absolutely everything you need to make a first batch except for the boiling pot. The Mr. Beer will also get you started on the right process for extract brewing with boiling the malt and adding additional ingredients in some of their recipes. You will be very limited in your beer making if you just always use the no boil beer in a bag stuff that the Beer Machine sells. Just my .02.
All that being said, I just looked at a newer model of the Beer Machine that adds a bottling attachment. That model actually looks pretty good to me since it encourages you to bottle the beer after fermentation is complete and it is an enclosed system to boot. I still think the cost is a bit high for it, but if you are going to get one, get that one. I would still suggest getting some beer kits or malt and doing at least partial boils vs. the Beer in Bag route.