When you activate The Heart of Life, it turns out that movement does not influence the effect of the activation in any way. In fact, you can activate The Heart of Life while running from the battle and it will in no way slow you down or affect your movement.
On the other hand, when you are moving, activating the Wand of Speed stops your movement and often results in your DG engaging whatever is persuing him/her.
This seems somewhat awkward and counter intuitive. Wand of speed is used when you want to run. So, stopping an already moving character when they use the wand is quite a bad thing. On the other hand, many people already complain about the heart being overpowered, yet it is usable without any hinderance. It seems to me that putting a restriction on the heart that the user must stand still while recharging would be very reasonable. Or at least when you go to 'use' the heart, your character should stop whatever else it's doing.