Larger oceans would mean more dissolved atmospheric gas. I had no luck finding good estimates as to how much atmosphere is dissolved in the deep oceans overall, I was able to do a very crude calculation using this website and estimates that there's about 50 times as much CO2 in the Oceans as there is in the atmosphere. Now, my estimate is hugely crude, but there may be an entire Earth's atmosphere, both Oxygen and Nitrogen trapped in the oceans. The deep oceans hold a fair bit of Oxygen and Nitrogen so by making the oceans bigger, the effect might be a thinner atmosphere. 10% thinner? 20%? 5% I couldn't guess the amount, but something somewhere in that range seems probable.
Regarding deep ocean currents, it's difficult (perhaps impossible) to say how currents might change. In general, ocean currents, while not simple, seem to follow fairly simple patterns. My guess is that the amount of depth you've added isn't enough to change that, though if you were to make oceans significantly deeper, you might get a few layers of circulation, not the three, sometimes four layers we currently have. (see pictures).
Larger, deeper oceans would also provide a greater heat sink that would take longer to warm up or cool down with the rise and fall of glacial periods. It's possible that there would be no glacial periods with these changes, but predictions get kind of speculative there.
That's all I can think of. I invite corrections and additions.