I see nothing wrong with the generated font files in either case. For this particular font there shouldn't be any difference between the two. When forcing the offsets to zero BMFont will embed the offsets within the quads themselves, and inspecting the font files I can see that this was done.

The difference you see might be a case of rounding errors when drawing the text. Either with the texture coordinates, or the placement of the quads on the screen.

For reference, here's the code I use to draw text with:

void CFont::InternalWrite(float x, float y, float z, const char *text, int count, float spacing)
{
    if( render->GetGraphics() == 0 ) 
        return;

    int page = -1;
    render->Begin(RENDER_QUAD_LIST);

    y += scale * float(base);

    for( int n = 0; n < count; )
    {
        int charId = GetTextChar(text, n, &n);
        SCharDescr *ch = GetChar(charId);
        if( ch == 0 ) ch = &defChar;

        // Map the center of the texel to the corners
        // in order to get pixel perfect mapping
        float u = (float(ch->srcX)+0.5f) / scaleW;
        float v = (float(ch->srcY)+0.5f) / scaleH;
        float u2 = u + float(ch->srcW) / scaleW;
        float v2 = v + float(ch->srcH) / scaleH;

        float a = scale * float(ch->xAdv);
        float w = scale * float(ch->srcW);
        float h = scale * float(ch->srcH);
        float ox = scale * float(ch->xOff);
        float oy = scale * float(ch->yOff);

        if( ch->page != page )
        {
            render->End();
            page = ch->page;
            render->GetGraphics()->SetTexture(pages

);
            render->Begin(RENDER_QUAD_LIST);
        }

        render->VtxColor(color);
        render->VtxData(ch->chnl);
        render->VtxTexCoord(u, v);
        render->VtxPos(x+ox, y-oy, z);
        render->VtxTexCoord(u2, v);
        render->VtxPos(x+w+ox, y-oy, z);
        render->VtxTexCoord(u2, v2);
        render->VtxPos(x+w+ox, y-h-oy, z);
        render->VtxTexCoord(u, v2);
        render->VtxPos(x+ox, y-h-oy, z);

        x += a;
        if( charId == ' ' )
            x += spacing;

        if( n < count )
            x += AdjustForKerningPairs(charId, GetTextChar(text,n));
    }

    render->End();
}

The complete code can be found here: http://svn.code.sf.net/p/actb/code/trunk/source/gfx/acgfx_font.cpp

Regards,
Andreas