What affects the surface characteristics of cumulus clouds?
No, clouds don't really have a 'surface' that could have tension like a body of water. The different looks in these two examples (left Cumulonimbus Calvus and right Cumulus Humilis) are greatly dependent on how they have formed and how are they evolving now.

The large Cumulonimbus is still growing in a relatively rapid speed. The cloud is reaching higher and higher upwards carrying moist air. The moist air due to turbulent flows and expanding of the rising air gets mixed with the cold air and instantly forms/extends cloud as it reaches saturation (saturation is reached with less water in colder air and air is colder in higher altitudes). If there wasn't the expansion then flows of dry air to the cloud would desaturate the cloud and more small scale variation could be seen as in the Cumulus Humilis. Also the Cumulonimbus being much larger and further away looks different just due to distance. The steady state like situation of the Cumulus Humilis where it isn't growing (perhaps a little on the top) and the fact that the lower atmosphere has stronger turbulent motions equals to the appearance where more cotton candy pieces 'drift' from the cloud.

Neither of these are ice droplet clouds (they look different just because they are made of ice and not water droplets), but all clouds that are in freezing temperatures have some very small percentage of ice in them too. The Cumulus Humilis might be below 0 Celsius and the Cumulonimbus definitely is at some height. A crude estimate is that temperature drops 6 Celsius every kilometer. The base of both clouds is probably somewhere between 1 and 2.5 kilometers and the Cumulonimbus might reach over 10 kilometers.