Some of the Scholars such as Ibn Rajab and other than him have mentioned that the fasting that is done inside of both Shabaan and Shawaal are more excellent than any fasting done anytime outside of the month of Ramadan. This includes the fasting that is done during the other sacred months, even the month of Muharram.
As a matter of fact Ibn Rajab (may Allah have mercy on him) mentioned in his book “Lataaif al Ma’arif” that the fasting that is done right before and after Ramadan (the obligatory fasts) are like that of the Sunnan ar Rawaatib (non obligatory sunnah prayers tied to the obligatory prayers) that are done before and after them. They are not only a completion of the the obligatory prayers, but add to their excellence. Thus the fasting done directly before and after Ramadan do have the same effects on adding to the excellence and completing any deficiencies within our fasting during Ramadan.
So seeing knowing the fact that the fasting that we do during this month will have a direct effect on the fasting that is done during Ramadan, do you not see that we should be doing as much as we can during this blessed month? May Allah make it easy on all of us and except from us our efforts. Allahuma ameen.