I don't understand the comparison. It seems like slope graphs and sparklines serve very different purposes. Both of the Tufte graphs in the piece (the "receipts of government" graph and the cancer survival rates graph) would not have conveyed nearly as much information if they were sparklines. The cancer graph is particular is magnificent.
The first set of bullets following the taxes graph clearly outlines what this type of graph excels at. I don't think those reasons overlap very neatly with sparklines; which are better at showing trends in time series data in a very small space. To me the key point about these slope graphs is that they show the relative rates between subjects very clearly. Sparklines do not do that as well, indeed they are often pretty compressed along the y-axis.
I don't think the parent poster was trying to say that someone should use a sparkline instead of a slopechart. I believe they were saying that they weren't impressed with slopcharts to the same degree as they were impressed by sparklines. If that is their sentiment, I agree with it fully. I found most of the examples non-intuitive. I had to really study it to try to understand what the chart was showing. That said, before I would say yea/nay, I'd like to try them with a dataset that I understand really well to see what they look like.
I thought the two examples that were actually created by Tufte were great, they made perfect sense and expressed the data well, while the other examples were kind of a mess. Partly this is because they weren't clear analogues to what Tufte made, trying to correlate two different pieces of data instead of showing how one piece of data changed over time.
The first set of bullets following the taxes graph clearly outlines what this type of graph excels at. I don't think those reasons overlap very neatly with sparklines; which are better at showing trends in time series data in a very small space. To me the key point about these slope graphs is that they show the relative rates between subjects very clearly. Sparklines do not do that as well, indeed they are often pretty compressed along the y-axis.