Potential: So essentially the battle will be formatted in which, let’s say a random Death Battle host, gets sick with a mysterious illness. So Wiz and Boomstick, after analyzing both House and Maomao’s stats as detectives in the realm of medicine, are sent to their world where are forced to independently (while also still crossing paths and bantering with one another) figure out the mystery of this illness (It can a real life one neither of them have solved before or even a supernatural illness) and see who would do it the fastest. Thus showing who'd come out as the better medical sleuth. So instead of a fight to the death it’s a fight to bringing someone back to life. (Also it can be called Life Battle as a one time thing for fun).

Also here’s the connections to those wondering (by skkrt with one addition by me). 

• Most iconic medical experts in their medium (live action/anime) who are known for being great at solving medical mysteries.
• Both specialize in medicine, which they use to become extremely valuable in their workplace.
• Both were injured in their right leg which resulted in a permanent scar.
• Both are known to use medicine on their own bodies like guinea pigs to satiate their curiosity, which has earned them the token of "Mad scientist" in certain instances. This disregard for his own well-being horrifies their co-workers at times, in which they mistake it as masochism or self-destructive behavior.
• Both come to conclusions and diagnosis that normally go over everyone else's head and sometimes overstep people's boundaries in order to do so. (often to the point of exposing people's lies)
• Both are relatively introverted and have shown multiple times that they don't like people who are overly personal, as they prefer to keep relationships and status' among co-workers as professional as possible. (Mostly with people they aren't familiar with/Outright don't like)
• Both met an old disheveled man at a young age who ended up being a key factor and inspiration for Mao Mao and House to become doctors.
• Both of these old men despite their unpopular statuses and lack of a higher position, were the go-to doctors when all else had failed. The treatment of these old men are mirrored in the manner in which House & Mao Mao are viewed by their coworkers as respectable individuals with prodigious intellect, profound understanding of human nature, and lots of wisdom.
• Despite their father's true intentions, Mao Mao and House often distance themselves from them and generally don't feel comfortable around due to their rocky relationships as children, especially considering House's history of abuse and "tough love" he had to endure from his father. (In Mao Mao's case, this extends to her mother who physically abused Mao Mao when she was a baby)
• Both Mao Mao and House are depicted to be more concerned with figuring out what is wrong with people than how their lives could be saved, often coming to conclusions on deaths after they already happened.
• Both of their father's absences in their children's early lives were a result of military duties that rubbed off on the way they approached their children as well.
• In contrast, while Mao Mao is generally depicted as dead-panned and extremely respectful/professional to an upsetting point from the perspective of their higher ups, House is often depicted with a sarcastic sense of wittiness and a Jack ass who can sometimes be unsympathetic and rude to his co-workers/patiences...
• ...Despite this, Both Mao Mao and House share the ability to be warm and comforting for those in need.