In terms of skill, these two have gone back and forth through out the years. Their first encounter, was a long fight in which they were dead even. They were perfectly stalemating each other until robin intervened and gave Bruce a slight edge. Later on, after the Knightfall arc, Batman actually went to Shiva to receive training in order to regain his physical prowess. He stated that they are mere equals in terms of fighting skill. Several years later, Batman beat Shiva in a Superman/Batman arc (with relative ease). To be fair she was mind controlled. Yet, statements through out that fight could leave someone to believe that Bruce has indeed outgrown Shiva in terms of skill, and he is now the better fighter.
Like i said, this is only in recent years. It seems that Bruce's more moderns arcs have him portrayed as being slightly superior to Shiva. For instance, against Prometheus (a man that gained the prowess of 30 of the worlds greatest martial artists via. downloading them directly into his ind through a helmet). Batman lost to Prometheus in their first encounter, when he was using a disorienting strobe effect to distract Bruce. In their second encounter the odds were evened (he still had the helmet) a Bruce was ale to best him in a hand to hand fight, before Prometheus shot him in the chest.
Shiva lost to Prometheus's understudy (with the helmet) in 3 moves.
For a while, they seemed even, but as of late, Bruce has been, in my honest opinion, portrayed as being superior to Shiva in terms of fighting skill. They are both two of DC's finest hand-to-hand combatants.
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