Google search ad and Bing ads are the same thing - they are both intent based platform meaning that people that got you there are in one way or the other interested in your service.
As an intent based platform, leads you find there are always hot and ready to hire you.
This means that the leads you generate from Google search ads and bing ads converts to a paid customer quite easily within a short period of time.
Differences between Google and Bing
Search volume and market share:
According to statcounter, Google worldwide market share for the search industry is 92.04%, followed by Yahoo with 2.67% (note: yahoo search is powered by bing) and Bing in third position with 2.39% share.
Based on the data, you can see that Google market share is far more greater than that of all it's competitors combined.
Average Cost per click (CPC)
According to wordstream, the average cost per click on Bing across all industries is $1.54.
Bing's average CPC is 33% lower than what we see on Google Ads.
This is as a results of advertisers taking advantage of a much less competitive ad auction in Bing Ads, which helps keep CPCs low in most industries.
Is Bing Ads good for law firms?
Bing because of it's small market share is only good for targeting worldwide and national campaign and to a lesser extent state campaign.
But when it comes to hyper local campaigns or targeting a city or county, Bing ads lags behind because of its small market share.
And because of this non-existent search volume for local searches, using bing ads for your law firm is a waste of time.
A law firms is a local business and it requires traffic from your city or county to be profitable.
Below is a screenshot of Bing and Google search volume for bankruptcy related keywords in Queens County, NY.

Bing search volume for bankruptcy keywords

Google Search volume for bankruptcy keywords
As you can see above, the search volume for bankruptcy in bing is just 10. That search volume is insignificant if you need a successful campaign.
But for Google, the search volume for bankruptcy is a whopping 880
Conclusion and Verdict
Bing ads is great if you run a national or state campaign. But if your law firm is a local business and only target a specific location, then Google Ads is your best option.