[Rosemary answers first] I think they are a bit different. Acceptance of Dukkha is actually Wisdom. Feeling with Dukkha, the Dukkha that comes, is more the Compassion.
Compassionate Understanding. If you put the two together then you have a powerful way to deal with Dukkha. Acceptance of Dukkha also involves Equanimity. So there are at least three aspects to this: Compassion, Wisdom, and Equanimity. We need more than just having Compassion for the Dukkha. Compassion helps, but it's the Wisdom that contemplates the Dukkha and understands the Four Noble Truths - and that is what is going to help us come to more Equanimity towards Dukkha, which helps us to come to more acceptance of Dukkha
[Steve adds to the answer] When we see Dukkha, usually the first response is that we wish it wasn't there. That is the Compassion. So that comes in, often before you can actually come to acceptance. We could say just the seeing of Dukkha and wishing it wasn't there comes first, then we understand the Dukkha and accept it - "Ok, it's here". And then we go about trying to work to solve the Dukkha. That's one way to look at it, as a kind of process.
If you remember in the regular retreat I describe a process that occurs, "We see something that's unsatisfactory, we have Compassion arising for it wishing it was not there, then Lovingkindness may arise wishing for peace and happiness to be there instead. Then, with the Compassion and Lovingkindness as our thoughts, we go about using Mindfulness to understand the situation and then solve it." So, there's a process there, and we certainly need the Wisdom, the Compassion, and as Rosemary said, the Equanimity as well. The whole process needs to be like a unit and this is one thing that some meditators don't understand; a practice being a unit of different aspects, different qualities.
There are some teachers who will stress, "be mindful, mindful, mindful, mindful; that's all you need." We heard one teacher respond like this to a question that a person was asking. They were having a lot of stress in their lives, they were having a lot of problems, they were having just a lot of general stuff going on, and all the teacher said was, "You need to be more mindful." When I heard that I kind of went "huh?" We were new meditators at the time, new Buddhists, but I still thought "huh?" We thought that was a general rule in the beginning of our practice. You had to be more mindful, be more mindful. And so, of course, as good practitioners, we tried to be more mindful but it didn't work that way because we were missing another aspect of the practice.
Eventually, we met a teacher who, when we explained some of our difficulties, he said, "You need to have more Compassion for yourself." And then it all started coming together for us. We started to see Compassion and Mindfulness working together, and that made the practice much broader.
Mindfulness by itself, or concentration by itself, there are a lot of teachers, some here in Germany, who stress "concentration, concentration, concentration", but that's just one little aspect of the practice. To have a broad practice, you need to have more tools to work with. If you limit your practice down to a one method, or only a few methods of practice, then it might not work so well. Like the hammer story I give during the regular retreat, if you can remember the hammer story: There are a lot of tools in that toolbox. You can build this fancy looking house, but if you only have a hammer, you just can't do as much. So to see the practice as a group of lots of different aspects, lots of different areas, is something that we want to develop so that we have a broad practice that will work twenty-four hours a day.