What all forget is the fact that Batman and Nightwig share an past with each other. No sexual, mind you, but they are used to fight as a team, in a most dynamic way, a duo par excellence. This would be the main advantage. And Nightwing is top if it comes down to Martial Arts and Acrobatics, he learned from the BEST.
Put it this way:
Scenario A:
IF it is a sudden H2H fight, then the girls are going to beat the boys.
Why?
Well, because Shiva is a killer of killers ....basically the best there is (well, that takes out a number of ppl who are better...eg Karate Kid, but you get my drift). Cassandra Cain is also the best there is (is she better than Shiva ...I say yes, others say no, it really doesn't matter .....point is she is also at top tier). There is no need to elaborate on their abilities (eg 'reading' what moves someone will make before they do).
Batman is a top tier too (is he better, I say no, others say yes, it is not really necessary which. Point is he is top tier). And so is Grayson ....Nightwing can clear a room of ninja with no problem (actually even Robin considers a group of ninja as a 'only a workout', and to Nightwing he doubts they can even make him sweat), thus he is also EXTREMELY good.
Problem is that Nightwing is nowhere as good as Cassandra, and no where as good as Shiva.
In a bloodlusted match, Nightwing wouldn't even be able to land A SINGLE BLOW on either Cassie or Shiva before his neck was broken or Shiva had driven her fingers through his skull and into his brain (her so-called 'Leopard Punch'😉.
With Grayson gone it would be Shiva and Cassie against Batman, and while personally I think either of them can take them out, I am sure that even those who think Batman can win solo would HAVE to agree that Batman cannot beat both Shiva and Cassie at the same time!
Thus, in a sudden H2H match the women would win.
And honestly I think they'd win it EASILY .....primarily because Nightwing would go down in an instant against either Shiva or Cassie, and once that was done it would be the two of them against Batman.
The weak link is Nightwing (as good as he is, and he is GREAT, he is simply not at Shiva's or Cassie's level)
Scenario B:
Your 'typical' Batman/Nightwing setup ....i.e gadgets, some prep, teamwork, etc.
In such a situation it is VERY possible for Bruce and Dick to win. WIth some of their gadgets, and laying up the area, they might be able to pull off some stratagem that allows them to win.
Thus, as long as they do not make it into a pure H2H deal they have a chance. Although the thing will be how to make whatever gadgets they use connect against people who dodge fullisades of bullets from point-blank range.
Although by gadgets i do not mean batarangs .....maybe some area effect device.
Conclusion:
Anyways, if it is a H2H situation I would have to give it to the women .....and I'd give it to them (wait for it) 10/10.
Why? Once Nightwing goes down (and he WILL go down, in less than a second) both would tag-team Batman. He goes down (even if we assume that the women are at least as good as Batman in H2H, then that would mean that it would be like ONE Batman fighting against TWO Batmen. And that is if they are all equal ....personally I believe they are better, but that is another discussion).
However, if Batman and Nightwing are allowed to use their minds, then the fight TOTALLY shifts the other way .....now Bat and Wing have the advantage, and a very serious advantage at that. It is now their element, and they can win this.
Thus it depends what scenario we are looking at.
A 'sudden' H2H encounter, or something that has some prep element added to it.
Which scenario is chosen can make this fight become a 10/10 for either side ....depending on the scenario.