There are pros and cons to either living situation. However, if you are trying to determine which can be more sustainable, that is entirely up to the denizens. I am finding that either one can be as eco-friendly as you make it. This also depends on your definition of sustainability. If you feel that you must live off grid and totally produce everything yourself an apartment isn’t going to work out too well. However, if you feel that a large part of living a sustainable lifestyle means living simply an apartment will work quite nicely.
Honestly, having lived in houses and now living in an apartment I feel like we are making better progress on becoming more sustainable. We have a smaller area to heat and cool. We were lucky that our complex has installed water conserving things in the bathroom (low flow toilet and shower head). We can have a small container garden. The biggest step for us is truly simplifying and decluttering our lives and belongings. Because we cannot produce enough of our own things it has also forced us to really turn to our local farmers and friends with gardens. We have had to become creative and really think about the purchases we make.
Living in a house was really more expensive, especially since we seemed find ones that needed work. That are not always set up for energy efficiency, water conservation or simple living. Granted the kids and I have had to change our approach and mindset regarding how much space we really need. Now I am not saying that it cannot be done, becoming sustainable while living in a house, but it takes cash flow, time and skills that not everyone has. In our situation it was more a lack of time and cash flow that hindered us. Finding a less expensive place to live (I do not recommend having to do so under the same circumstances we did), really getting down to need vs want and learning to take advantage of local producers, artisans, etc really does give apartment dwellers the option to live sustainably.
Light, Love and Peace!