Beneficial bacteria that creates the nitrogen cycle in your tank is happy to live anywhere it can. It actually can attach to the glass walls of your tank, your decorations and the surfaces of the gravel in the bottom of the tank. It does not care whether it is in a sponge or a ceramic cylindar or a bio-ball or a bio-wheel. It is happy.
Ideally, your bacterial platform should be on a surface that you do not regularly change or clean much. To depend on a cartridge to carry your entire cycle, and then regularly throw the cartridge out is not a very good idea. That is why the various media is excellent. Let the floss filter out the large waste, and the media contain the bacteria.
To encourage more bacteria to grow and live in your tank (more bacteria mean more ammonia that can be processed, means more or larger fish can be supported) you need to provide them with lots of surface area to colonate - surface area that is exposed to oxygen from the water. The best surface areas for the bacteria are in a filter that has the water flowing through it. The water flow constantly carries the ammonia laden water past the bacterial colony, as well as the oxygen contained in the water.
Ceramic cylindars, sintered glass, lava rock, sponges, etc. all have lots of pores making miles of surface area for the bacteria to colonize. These are all excellent platforms for your bio-cycle. Polished rocks, glass, inches of gravel (anything other than the surface gravel does not get enough exchange of water and oxygen to properly support beneficial bacteria), and a thin layer of floss can hold some, but not as much, of the beneficial bacteria.
I do not know exactly what is in a "bio-bag", but I suspect it contains pieces of lava, sintered glass or some such platform. This is actually fine. If you would prefer to replace it with a sponge, you are certainly free to do so. A sponge, also, has miles of surface area. I do know know which one has the greater platform area for the bacteria - I would need to know what was in your bio-bag. I find that the "hard" media holds less gross waste than a sponge, but much of that depends on what is where in your filter. Because of this, I prefer the "hard" media. That is my personal preference. If you like a sponge - go for it. Just realize that it may not be much better - just different.
Try putting the sponge in the filter and dropping the bio-bag into the tank for a month or two to colonate the sponge from the bio-bag. That way you should not bump your cycle too much.