I have a Roland RD-700 at home. Our church has a 6' Yamaha Grand (which I donated because it was defining where I could live because of the space required). I love playing and practicing on my Roland since, as an apartment dweller, I can do it at anytime, but I still love playing a real acoustic grand at church, or anywhere. Though the RD-700 has a weighted keyboard, and I usually set the internal setting to super heavy, it still does not have the weight that the Yamaha has. I find it to be somewhat of a workout at times. But it always feels good.
A part of the difference between the two is that the nature of an acoustic piano uses the entire room as a part of the instrument. Sound radiates all around from both the top and bottom of the sound board and therefore is omni-directional. The sound of a digital piano comes from particular sound sources that are usually directed toward the audience.
As far as pedaling, I find that I do have to be careful because on the Roland, I can keep my foot on the damper pedal for longer before it gets too out of control. An acoustic instrument actually has a range of possible pedalings.
Possibilities with an acoustic damper include.
1.) Just keeping your foot slightly on it enough to not sustain but to "lighten the action" What this does is get the dampers on the start up so that your fingers do not need as much effort and is particular good on long passages of fast sixteenth notes.
2.) "Half-Pedal" which will somewhat allow a bass line to continue to sustain while damping the treble. There are actually several degrees of this type of pedal before the dampers are all of the way up.
3.) a Flutter type pedalling which helps to thin out some of the blur without completely stopping all of the sustained tone.
One thing to try on an acoustic instrument is to find how far down you actually have to push to completely lift the dampers (it is seldom all of the way to the bottom) and how far down it takes to start lifting the dampers to cause some sustain effect. Then experiment with different effects possible in those points in between.
You may need to adjust the damper mechanism if it is too sensative (the slightest touch causes some sustain) or if you have to go all the way down. This is done on grands with a nut at the end of the damper rod and is not too difficult.