I typically play the way you described - turning off computer trading, handling real-life transactions on my own.
Although OOTP has made great strides in the historical area the last couple of versions, I've found it's never quite going to fulfill my needs for the way I like to play. It's not the game's fault as it doesn't purport to be a replay sim like Action or Diamond Mind. Starting with the 2007 version (and continuing with OOTP9), I attempted a "History of Baseball" replay beginning in 1901, handling trades on my own, etc. It's a bit of an undertaking, and the results were disappointing as time went on. I found a lot of fringe/unknown players having career years more often than not...plus teams that were truly awful in real life ended up winning the World Series, etc. - something that made little sense since I was maintaining virtually the same rosters as in real life. Keep in mind, I don't want an exact replay of history - but do I want results that are plausible and within the realm of reality.
Although I stuck with my league for a while, overall the whole thing didn't feel right and I finally gave up in 1907. For some more specific info about my concerns, check out my comments (and others) in this thread:
http://www.ootpdevelopments.com/boar...-question.html
Anyhow, for historical play, I recently moved on to the other game you mentioned, and it's really top-notch with a lot of features I wish OOTP would employ...and because of the convenience of these features, the overall experience is a lot more fun.
I'll still use OOTP for fictional play (it's clearly the best for that!), but for historical gameplay, the other game is far superior in meeting my needs.