If you are using Greatswords in any role, I would suggest you keep your BSB. A unit of Greatswords with two detachments, with a combat BSB, can hold a flank for a long time. The BSB allows them to re-roll a failed break test, and with their stubborn ability, this makes them close to unbreakable. What I mean by a "combat" BSB, is that he has probably AOM and the Sword of Might. This allows the BSB to get some whacks in against the enemy before they eliminate too many greatswords for them to be effective. The secret of Greatswords is flanking detachments, so they can win melees, and something that swings at normal I so that they don't get so severely damaged that they lose too many guys to win the melee.
Recently, I put my Battle Captain on the Pegasus in with my GS unit when I saw it was about to be charged. This gave me some swings to assist the boys and since he joined the unit it made him effectively stubborn, just in case something went badly. (I may be wrong about being effectively stubborn but it didn't come up in the game, so I didnt' read it to check it out).
A little OT, but I have found that part of my deployment plans have been flawed lately along with the weapon selection for my EC. It seems that placing my Griffon unit on the flank, my greatswords in the middle with the EC, and the flagellants on the other flank is a better strategy. Most folks won't charge a Griffon unit or a unit of flagellants either one, so they beeline for the unit they can at least have a chance to beat the Greatswords. Having Von Aichmaan, put away his beloved greatsword and Speculum and giving him the Holy Sword of Sigismund, makes this unit very hard to beat, especially if the free company detachments get into combat. The Sword allows the EC to take out a few chargers, along with the free company. This will usually result in a few less swings from the enemy, giving you at least a chance to swng back with your greatswords.
This same strategy could work for a BSB with the Sword of Sigismund. Hopefully, he can kill the enemy troops in contact with him before he swings, keeping him alive, assisting melee, allowing re-rolls, despite being naked. His 4+ AS and 4 T, swinging first, and a higher than normal WS, will make him survivable to most units.