Answer: Each kind of seed-starting container has its advantages. Read the points listed below, then think about what you are growing and how and when you plan to transplant your seedlings outdoors. The best choice should stand out.
Cells: These are trays split into individual compartments. You would sow several seeds per cell, then cut off the weakest seedling(s) leaving just one seedling growing in each cell. Each plant’s root system would develop within its own cell, making it easy to transplant them individually to specific sites or containers. (Their roots do not become tangled.) It is easy to remove seedlings from cells if you don’t want to reuse the tray; you can just push the bottom of the cell up until the seedling pops out, rootball and all.
Pots: Pots have mostly the same advantages as cells. You can sow the seeds and trim the seedlings to end up with one plant per pot, each with a distinct root system. Pots aren’t as flexible as cells, so you can’t just push/pop the seedlings out at transplanting time. On the other hand, you can choose pots that are larger than cells, which are typically quite small. This is an advantage with seeds started very early. If those were started in cells, they would likely require transplanting to a larger pot before the time came to move them outdoors. Starting with a larger pot to begin with avoids this middle step.
Flats, or trays: These are shallow, rectangular pans with no dividing lines, just their four perimeter walls. Flats are a good choice if you’re planning to transplant the seedlings into the garden as clumps. You can scoop out a grouping of seedlings all at once and plant them in a large, wide hole together. Otherwise, you would need to disentangle their roots, which could be difficult.
There is a fourth choice for seed starting—the plantable pot. These can be pellets that expand into a mesh/peat-mix pot when soaked in water; biodegradable peat pots (Jiffy is one brand) or CowPots that you fill with planting mix; or homemade versions created from newspaper with a mold. The added advantage of these containers is that they can be planted in the ground with the seedling; there is no need to remove the seedling first, because the container will ultimately break down on its own.
Image attribution: Michael Bemmerl. Rights.