Why should I have to choose between compound sentences and compound predicates?
Solution 1:
You have the extra option for putting added emphasis.
It's not very apparent in your example. Allow me to propose another:
"I walked up to him and shot him."
This sounds like something a serial killer would say. I is too far removed from shot. No biggie, all in a day's work!
"I walked up to him and I shot him."
Depending on the context, this could imply my shock/incredulity/pride at what I've done. Shooting someone probably isn't normal for me. Putting I near the verb shot emphasizes the subject and the action better.