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(Note that with 3.5's change of the bane property from +2-equivalent to +1-equivalent, these two properties are no longer necessary.)
Bane in D&D 3.0 is a problematic weapon property. It
costs +2, deals +2d6 damage against one type of creature, and is +2 enhancement
better against that creature. However, for that same +2 you could put two
energy properties (such as frost and shock) on a weapon and
deal +2d6 to (essentially)
every creature at the cost of not being
able to bypass DR so easily (although the energy damage bypasses DR). In
almost every situation, you'd rather have the frost shock weapon
instead of the bane weapon, certainly when fighting non-bane opponents,
and in most cases even when fighting the appropriate bane creature. Compare
also to holy (also a +2 property), which deals +2d6 to evil creatures
(which are going to be about 50% or more of your chosen foes, compared
to maybe 25% or less for the limited use of bane). Bane is
probably too expensive at +2.
Now, the "bonus +2 enhancement" property of bane is nice, but you'd get that if you just paid for the +2 normally (since bane is already +2), so that's just evening out what the weapon would have anyway if you just pumped the enhancement bonus, so it's sort of a wash. It also doesn't take care of the fact that there are going to be creatures out there with DR better than X/+3 (solars are one, and I wouldn't be surprised if there were evil creatures in a future monster book or the Epic-Level Handbook that had DR X/+4), and so a +1 bane weapon still isn't helping you as much as it should for its cost.
So, here's what I propose: Change bane so it's worth its full +2 cost, and introduce a weaker version of bane that's only +1. Why do the latter? Because expensive weapons are a hassle for DMs because once you're beyond +3-equivalent, only very high-level NPCs can afford to have them and so it's difficult to equip them in the hands of NPCs without being a disproportionate treasure reward. Additional weaker properties allow more +2-equivalent items to be in circulation (at 8,300 gp or so, it's a reasonable bit of equipment for a 8th- or higher-level NPC).
Part of me wanted to call this a grudge weapon instead of lesserbane, but it would sound a little silly on an otherwise heroic weapon. I made lesserbane one word just so the formal writeup of the weapon doesn't end up a long string of words--imagine a +1 evil outsider lesser bane longsword.
So the greaterbane weapon is made up of
one +1 property (lesserbane) and another +1 property (sure striking
from Magic of Faerûn and Sword & Fist, which I
had created independently and named peerless before I found out
S&F already had such a thing ... note that again I prefer
the single-word name for the property, but oh, well). Technically this
means that the greaterbane quality as presented here doesn't need
to exist; however, creating this property means that if you have a bane
weapon, you can just swap it out for greaterbane and it's still
the same price, and you don't have to rename it a "sure strikinglesserbane"
(Originally I had called this property bane just like the original, but it was suggested I rename it to avoid causing confusion about which version of bane you meant.)
I'm probably going to want to go back and change some of the Blades of Faerûn anyway (to lesserbane instead of bane) because I'd rather they be cheaper and more readily available than expensive and more powerful.