Choosing Between Mindfulness and Compassion Meditation Basically, I have tried for some time mindfulness meditation. I have also tried compassion meditation. 

In mindfulness meditation, my mind becomes very still, with few thoughts, but outside of meditation the mind remains so. My thoughts outside of meditation are quite abstract, but I am perhaps stunted emotionally and in terms of visual images. I don't feel my mind wanders too much though.

In compassion meditation, I visualize loving-kindness and compassionate images, and I usually end up crying or feeling positive affect in my body. It is nevertheless quite difficult for me to visualize vividly.

How does one decide which type of meditation to engage in? Would both mindfulness (focused attention) and compassion generate some type of meditative concentration?
In so far as your quesstion is about Meditation, I cannot say anything. 
But if you were to mean Buddhist meditation, then I can say the following-
The meditation technique which Buddha taught, which is the teaching of the Buddha and the basis for all philosophical schools, is Vipassana. Other techniques serve as efficient and helpful techniques, depending on the individual. So for example, if someone is unable to meditate because they cannot concentrate their mind, they would be suggested some technique (like anapana or samatha {which in fact is considered as a pre-requisite for Vipassana by many schools}) or a skill in daily life (such as reciting a particular mantra or counting the number of beads in a mala) that would develop some concetration, which will allow them to practice vipassana. Or if a person were too obsessed with physical beauty, with lust- so much so that they cannot practice vipassana, they would be advised to meditate near the dead bodies. 

Vipassana involves not only the establishing of the four-fold awareness and the insight gained from it, but also leads to one becoming more compassionate and more aware (mind-fullness). What I mean to say is that, the two aspects you have asked about, comapssion and mind-fullness are not seperate- they go hand in hand- one helps in developing the other which helps in developing the first. But it is possible that one may have some problem in developing mind-fullness or practicing compasssion. Therefore, in such cases, as per the understanding of the teacher (spiritual guide, elder monk) certain technique of meditation (like verbalization or visualization) which is not Vipassana, would be suggested in that particular case, so that the meditator can continue making progress.

Only you would know where you are in your progress and only you would know what problem you have with regards to you meditative practice. I suggest you read further literature so that you can understand in your own way of thinking and continue practicing. Do not get involved with questions to the extent that you stop meditating at all. Neither ignore the questions that have occurred to you- and if you cannot answer them, then consult a senior monk, or your guide.