"I know who the good lawyers are and who the lawyers are who are specialists in whatever area," McGraw said.
McGraw also argues these outside firms and their attorneys bear the risk of fighting tough and sometimes lengthy battles against well-heeled interests. If the outside attorneys lose, they don't get anything and the state loses nothing. If they win, they get something and so does the state.
McGraw said he wasn't sure how he could get the same results he has gotten over the years by doing it another way.
"If you were involved in some litigation, let's just say, a divorce action," McGraw said, setting up an example of how a different process might work. "So, what you'd want to do is run an ad in the newspaper in which you say, 'I mean to sue my spouse for divorce and what I want to find is the cheapest lawyer to do that, bidding is open and all bids will be considered, and by that way, I shall select who will represent me in the divorce'?
"Some people may want to do that; I wouldn't recommend it."
Morrisey said there were ways to open up the hiring process to make it more transparent.
For instance, he said there could be lists of lawyers who routinely do work for the state based on specific criteria.
Morrisey also said he might end up being limited in how much legal action he could take against the federal government without a like-minded governor or agency as his client.
"There are certain independent authorities that the office of attorney general has," Morrisey said. "But, at the same time, as a practical matter, you don't want an office of attorney general running out there on their own without having the political, policy and legal support from the governor and the agencies - this has to be a collaborative effort."
Still, he said he would do more to fight the Obama administration - which, of course, may not be in power next year - than McGraw has done.
"It's my belief that Darrell McGraw's endorsement and support of President Obama has compromised his vision of the office because we needed someone more willing to challenge these federal regulations, and Darrell McGraw hasn't been willing to do that," Morrisey said.
One of McGraw's special assistant attorneys general filed a lawsuit on behalf of former Gov. Joe Manchin against the Environmental Protection Agency, but Republicans say there are more legal actions McGraw or current Gov. Earl Ray Tomblin should be taking.
The pair also sparred over the transparency of the office.
It's currently hard to track how much outside attorneys are paid when they take their cut of a lawsuit the state settles or wins.
McGraw said the information is public in court records. But those records could be in any of a number of courthouses across the state and are not centrally housed by McGraw for public consumption.
Morrisey said he would do more to let the public view how much money outside attorneys are receiving.
Morrisey also said he wanted all settlement money to be given to the Legislature.
McGraw said 99.9 or 99.7 percent of all the settlement money already does go back to the Legislature.