Many bloggers online believe the former one is right. I spent more than half an hour to check and finally I can obtain the conclusion as:
The correct answer is: 功多藝熟.
You can hardly find the comparison of 工多藝熟 and 功多藝熟 since most online dictionaries do not contain these two phrases.
Finally, I can locate one representative website from the Ministry of Education, Taiwan which contains over 40,000 set phrases.
Its most useful link is enclosed below:
http://dict.moe.gov.tw/chengyu/mandarin/fulu/report/download.htm
There are 4 files available to download, all in Excel format.
We can find the details in the following:
File number: n4
Item number: 41917 功多藝熟
From this internationally recognized national website, we confirm that 功多藝熟 is the correct writing.
Hope I can help you.
參考: Mathematics Teacher Mr. Ip