I think both still have their place depending on needs. A couple other things that are often not considered in the digital versus analog discussion... Depending on what your definition of "affordable" is, your experience may vary.
Many older analog oscilloscopes have better Y-axis sensitivity ranges, some even down to the 10s of microvolts. (Tek 502, 5030, 5031; 5A22N and 7A22 plugins, et. al.) Good luck finding much better sensitivity than 5mV/div on affordable modern digital kit. Granted, not something a lot of people need all that often, but if you do... Which also brings up another thing: Differential input plugins for older analog oscilloscopes can generally be had for a fraction of the price of just a differential probe - often times you can buy the whole scope and plugins for less than a single differential probe.
Many affordable modern digital oscilloscopes do not have the ability to slave 2 different time-bases to different channels and display them along side each other. Again the keyword here is affordable! (Tek 547, 7xx4, et. al. can do this if the correct plugins are used)
Most affordable modern digital oscilloscopes are 8-bit resolution on the Y-axis. This means if you are measuring a signal and have the scope set for 1V/Div, the best resolution you're going to get is ~31.25mV, assuming an 8v x 10h graticule and my math is right (8V / 256 steps or 8 bits). That means if you have a small amount of noise riding on your signal, it's going to be harder to see. Again, whether or not this matters to what you're doing is another story, but it can make a difference sometimes.
As was mentioned before, X-Y mode on analog just seems to work better.
Aliasing. It even happens sometimes when using the "Auto-set" feature, and that can be frustrating for anyone who hasn't trained themselves to double-check the time-base readout on a digital model - that or give the time-base wheel a spin back and forth just to verify.
That said, I love the measurement capabilities and a lot of the other features on the digital "dark side," especially if your digital kit has a built in function generator. Having the ability to do bode plots is definitely nice to have. Also the having FFT capability, generally nicer cursors, automatic math functionality, etc. all are pretty awesome. Also "affordable" buys you a lot more in the digital realm nowadays than it used to.
At the end of the day, it's all about what you need the oscilloscope for in the first place. If you're troubleshooting digital circuits, using an analog model is bordering on masochism. If you're troubleshooting power supply noise, that can be a very different matter.
Just my $.02 worth.