It's very accurate in the sense that if you read the whole series, you'll know an astonishing amount of detail about the period of about 110 BC to 27 BC in Rome, and few if any details are provably wrong, at least. But it's true that, aside from a general tendency to pick the interpretation that makes for the best story, she's an unabashed fangirl for Caesar, and later to a lesser extent Antony and Cleopatra.

The first two-three books are probably the best, because they mostly deal with Marius and Sulla whose rivalry is depicted in a more balanced way, and most readers are less likely to know that period in such detail already. By the time you hit the final book, titled simply 'Antony and Cleopatra', you're treading well-worn ground to say the least.

I enjoyed Adrian Goldsworthy's biographies of Caesar and Antony/Cleopatra respectively (see my reviews here and here), as well as his book on the later decline of Rome.

For the period inbetween, the early emperors, you could do worse than to go back to the primary sources for all later works, Suetonius' Twelve Caesars, or Tacitus' more detailed works on the mid-1st century AD. A modern work might be a bit more accurate / less biased than Suetonius though.

No idea on a single book covering the whole period, but I'll be interested to see if others can name some. Would be especially interested in the second century BC.