Let's assume that the character has full BAB. And +5 enhanced weapon. Than he would get total 25 AB at the 20th level. At the same time he would have 11 armor bonus (8 + 3 for mithral full plate) +5 armor enhancement bonus, tower shield with 4 shield bonus and +5 shield enhancement bonus, natural armor bonus +5 and deflection bonus +5, totally +35. So he would hit his own copy only on natural 20 (25 + d20 against 35 + 10).
Well, character could invest in boosting his attack attribute, strength, or dexterity for weapon finesse users. But he could equally boost his defensive attribute, replacing +5 mithral armor with monk's belt and bracers of armor +8. If he could boost his wisdom with buffs at least to 24 (in addition to boosting dexterity), he would get equal armor bonus, but without dexterity cap, so the character could grow his defence attribute at the same rate with offence (and if he is a weapon finesse user, the attributes are the same).
Monk's belt could be used together with shield bonus, just employ persist metamagic on the 1st level spell Shieldbearer from the SpC.
There are feats that increases AB, but there are also feats that allows you to use armor more efficiently, or use TWF for defence. So it is a draw.
So, how a high level character is supposed to hit his own copy?