I like the ergonomics of Analog. Tuning is easy to do, with just a turn of the knob. Also, it's easy to see the relationship of the tuned station relative to it's respective location on the tuner dial with just a glance. Fine tuning is done by ear rather than with the eyes -- hard to do on a digital tuner if you are driving. Also, nothing beats the look of a top quality analog tuner dial. Wide, nice glass, attractive graphics that light up, smooth operation, weighted tuning knobs, etc. Cheap tuner dials, on the other hand, really really suck. You know the kind -- thin cutout with a thin needle, no backlighting, dial markings silkscreened right onto the front of the device.
I like the attractive looks of a well designed digital dial. I also like it's precision and accuracy. But since there is nothing more to a digital tuner than a set of digits, it's easy to get lost in a large radio so a nice, large display is a big plus. A lit digital tuner is bitchin, especially flourescent ones, ala RX7200. LCD ones take a far backseat. Small LCD ones, like the ones on modern eggs can take a backseat in the tail end of a bus. A big bus. Some of the tuners on home hi-fi pioneers and Sansui's of the late 70's and early '80s have really attractive digital tuners. On digital tuners, I far prefer a knob rather than up/down buttons.
Reception: There is a misconception that analog tuners get better reception than digital tuners. This is a non-issue and NOT the case. The front end of any AM/FM tuner is analog. To prevent confusion, we are talking analog signal and not analog display. Reception ability has no relationship to how the displayed interface is designed. For the most part, digital tuners offers more precise tuning. Where an analog tuner can appear to have better reception is when a low quality tuner is out of alignment. But the biggest reason why analog tuner appear to tune better, especially in areas of poor reception is due to the fact that digital tuners makes more frequent use of technology such as muting circuits. A muting circuit silences the audio when a poor RF signal is received. The intent was to prevent staticy type noises from weak stations to "dirty" the audio quality or annoying the listener. Therefore, when a poor station is received, the muting circuit will "mute" and quiet that station. It can also cause the station to go on/off again as the signal strength drifts over/under the RF strength threshold set for the muting circuit. This phenomenom is also present in analog tuners as well, when this feature is present and active. Some tuners have a muting on/off feature. Others such as the Conion C100F appears to have a muting circuit built in without an option to turn it off. You know you have this feature when the radio goes silent between stations. Tuners that present static or white noise between stations do not have this feature, or have it deactivated.
As for boomboxes with a combined analog/digital display -- the very beautiful and rare Sanyo M-X820/824 comes to mind.