Strictly business... well I would agree that Michael took everything as personal as his father did. I think that both of these killings could be construed as business and as personal.

On a business end, the most superficial layer, the Corleones had to take Solozzo out, he would have tried for Vito again and that would not be good for business at all. Also, it’s just standard policy in the Cosa Nostra that if someone strikes at the leader they are dealt with swift vengeance. McCluskey, the corrupt cop had enough pull, was deep enough in Solozzo's pocket and if it weren't for Michael showing up at the hospital, he would have had a big part in the finishing off of Vito Corleone once and for all. McCluskey posed enough of a threat that it was warranted that he would be taken out, he could have used his power to help Solozzo and his men plan another hit.

Solozzo had to be dealt with, McCluskey was outed because in a limited sense he was Solozzo’s body guard and would have struck back at Michael and had to be dealt with. It can be also thought that McCluskey involving himself in the second assassination attempt on Vito by pulling his officers off guard duty was in a very real way getting himself mixed up in business.

The personal aspect overlaps this too. Solozzo tried to kill his father and McCluskey hit Michael and was responsible for pulling the cops off the duty all personal swipes at the family.

Michael also realized after the hospital incident that his role in this, whether he liked it or not he was more linked to the destiny of the family and his father that he would have liked. He consigned himself to this fate. Part of the choice was this aspect of being sorta forced into the situation, part of it was the business aspect and part of it, I think superceding the business aspect was his personal vendetta.

I think his personal vendetta between Solozzo and McCluskey and the opportunity that presented itself acted as a bridge that allowed Michael to cross from his life as an outsider as he placed himself in into the life of a insider within the family.

Would anybody in his position have acted much differently? I wouldn't, something had to be done to protect his family and his father, so he did the deed and the rest is history.

It should be noted that the word family is very important as well. Although the words "business", "family business", "the family", etc... are used it is clear that there is a business as well as a personal aspect that links any memeber to his "family", even more so the actual higher ups.