It really depends. I do both. A lot depends on the size of each, relative to one another. Width of the hone, relative to the length of the blade, makes a difference. For me, narrower hones are often easier to 'take to the blade', with the blade being braced or held in a fixed position. Very easy to focus on narrow sections of a blade this way, such as with the tip and heel, which almost always need 'extra attention.' On the other hand, even with a 'small' credit card sharpener, it's wider area usually is conducive to laying it flat, and moving the blade across it. With this style of hone, being very thin, it's a bit safer too. A little too easy to cut yourself, trying to move & control a thin & short hone, held by the tips of your fingers.
Hones like DMT's Dia-Folds, with their built-in handles, can be used very effectively either way. It's one reason I like these ones a lot; they were designed very intuitively, to accommodate the different styles & preferences of users. Can use it like a file on wood, with the blade under the hone, or you can brace the end against a bench or table, and use it more 'conventionally', drawing the blade across it. I still experiment with different holds on mine, and find reason to like it, no matter which way (hone-on-blade, or blade-on-hone, both right and left-handed).
And obviously, much larger hones are almost always easier to use, and more effective, when laid steady on a bench.