Not only do you need to consider how to avoid being penalized by Google (possible but unlikely). Far more you need to be sure you're not penalized by the readers/followers of the other blog (much more likely, depending on how you handle the transition). Google rankings are cool and all, but the name of the game is those folks actually visiting those pages and reading those articles.
I'd say eventually it would probably be easier for administration to merge the two, but you don't have to do that right away. From a business standpoint, think about how most major corporations handle mergers -- as long as both businesses were strong, they usually don't immediately shut down one and make all the employees start working at the other one's offices. (Well, sometimes they do, but there's usually a lot of negative backlash that results...) In a lot of cases, they keep both businesses running while they evaluate the systems and processes, the personnel, the strengths and weaknesses of each business and over time merge the two -- if they're smart, keeping the best of each. Occasionally, they decide the two businesses serve different enough audiences and each is strong enough on its own to justify keeping them both as going concerns.
My -- keep both sites going for now. Spend some time thinking about how best to merge them (or if merging them is even a good idea). Be transparent. Let the followers/readers know about the acquisition (if you haven't already), but assure them nothing will change in the immediate future... then make sure nothing changes, at least in the short run.
Then monitor the traffic and engagement of the newly acquired site. Compare that to the traffic and engagement on your existing site. Patterns will become clear. You'll be able to see which pages generate the most traffic, whether the most popular pages on the "new" site mesh well with the most popular pages on your existing site, and how the visitor engagement compares between the two.
You may find it makes the most sense to keep both sites going. Or you may find it makes better sense to merge the two into a single entity, perhaps under your existing domain, or perhaps moving everything to the the newly-acquired domain instead.
If you decide to merge them, make sure you include at least the most popular content from both sites, with 301 redirects in place from the "old" URL to the new one for those pages that are moving from one site to the other. (You may also want to combine two or more pages into one to avoid overly redundant content. In that case, use 301 redirects from all the "old" articles on both domains, pointing to the new, merged content.)
It would also be helpful on articles that were moved or merged to include a brief, friendly "welcome, former [previous domain] readers" type message, ideally triggered when someone arrives at the page via the 301 redirect. The purpose of this would be to let them know that (even though they've arrived at what might be an unexpected domain, perhaps with a different look and feel than what they're accustomed to), they are in fact at the right place to reach the content they were seeking. It can also alert them if they were using a bookmark (browser or social) to get there, they may need to update their records to point to a different location for that article.
Again, this is just my ... YMMV. I'd be interested to hear what others have to say on the subject, as well.