For everyday use, modern gear is more reliable and provides a magnitude greater feature set.
They are an order of magnitude more convenient, but I am not sure about having an order of magnitude greater feature set. They have all kinds of automated measurements, which save time, but it is an oscilloscope, so I am more interested in what the shape of the wave is.
They are more reliable only because they are new and old oscilloscopes are old, but I doubt current DSOs will operate for as long. How many modern DSOs have failed because of failed storage or loss of calibration data? If something breaks, throw it away, and buy a new one.
Things which I would love to do with a DSO which would convince me to buy a new one:
1. Gated RMS noise measurements. My old Tektronix 2440 DSO does this perfectly. My analog oscilloscopes also do it perfectly, albeit not as easily. Some modern DSOs that I have tested simply return the wrong results, maybe from making the RMS measurement on the processed display record?
2. FFT noise density measurements - some very high end DSOs can do this, and as pointed out to me, many R&S models, although I am not clear how far this extends into their lower end models. I need to do a survey.
3. Frequency and phase response measurements - sorry, the current Bode plot thing is a joke, and not even a good implementation of a swept measurement. I want the superior FFT version which operates in real time. Some old DSOs support this, but I will probably have to give up and buy a dedicated low frequency network analyzer for this, which is a shame because it should be so easy on a DSO. Again some R&S models might support this, and LeCroy high end models.