Washing with soap will prevent an infection. Once an infection sets in, Neosporin will work well. It also depends on wound size and where it's located. Open wounds in joints should be flushed to prevent very serious infections, and probably should be followed by an oral regimen of Keflex, but I think in the wild if you get a serious break in the skin opening up the knee where you can see the patella, et al, it's best to flush it, apply a loose bandage to prevent more contamination and get yourself to a hospital asap so it can be X-rayed, cleaned/debridement, and sutured.

I carry a small spray bottle of hydrogen peroxide as I've found it actually works faster at eliminating small infections quickly. I may also follow up with a wash of betadine solution. This stops an actual infection in its tracks. Some don't like this method as they say it also kills some good skin cells. I think with a normal immune system, the dead cells will be replaced quickly and it's not a problem.

As for the wound healing time on a cut not infected, but with a topical antibiotic used to PREVENT infection, polysporin actually allows the wound to heal more quickly than neosporin. I have both, but the neosporin I use has a mild painkiller that has proven to be effective. Typically, I don't use it unless conditions indicate the need to lessen risk of infection. I just put a bandaid on it and let it heal itself. After a day or two, I take off the bandaid and let the air dry it out. (Again, under normal conditions -- always keep an eye on a cut until you know it's healing okay when you're afield.)

Also, you should look at the environment you are in. In humid, jungle like conditions, neosporin and other ointments work great, but in certain arid conditions flushing the wound with a betadine rinse is better. A powerdered form of neosporin can also be used for certain types of wounds.

You can't have everything with you, so I now carry the aforementioned small spray bottle of hydrogen peroxide, a few betadine swabs and a few quart size zip lock bags. I fill the bag with water, clip one bottom corner (small clip) and squeeze the bag to get an effective stream to flush the wound. This whole kit weighs little and takes up a very small space in my FAK.

As with all things we humans do, YMMV.