I have received my first DSO and have played with it a little bit.
Nice large screen and much smaller package overall than I had expected it to be. I have learned quickly what most of the buttons do.
Some great points:
Horz and Vertical auto-centre in a simple button push, auto-"50%" trigger, "autoset" and "autoscale" buttons so you can at least get a wave on the screen again, if you have messed up lots of other settings. I also like the "measure" button which allows you to display on the bottom of the screen up to 4 types of measurements on each channel, eg frequency, RMS, mean etc. Much better than trying to count rectangles and do mental math.
You can also set a limit of 20MHz on the channels so that you get less spurious noise.
It makes calculations easier because it understands the probe setting (1x 10x 100x etc) and marks the divisions accordingly, whereas on the analog scope I had to remember to multiply everything by 10.
There are many more functions of course, these are just first impressions.
Some criticisms:
When I "add" channel 1 to inverse channel 2 to make a differential measurement, it shows me all 3 curves, ch1, ch2 and the combined "M" (M for "math"). Unfortunately there no way to hide ch1 and ch2, and in this mode I really only want to see M, not 1 or 2. This is very annoying straight away.
The trigger function area should have another real button or two for very common things, eg "trigger source on channel 1 or 2", "trigger coupling" etc - currently you need 3 or 4 button presses to change triggering from ch1 to ch2.
When I want to zoom in and view a captured wave I only have one knob to move left or right, and it takes dozens of turns to move into the captured wave. There should be a "smart" move, like on my kitchen oven, where turning the knob quickly increases the step. Having said that, if you rotate the time base button, it zooms in and out centred on the middle of the screen so that way you can move to a specific area quickly.