Yeah, it can get skinny in a hurry. I always see a few hotdogs (really just guys that know the route) just get on plane and go!!! Speaking of that, with stern drive, while my draft be greater or less than with an outboard?
The draft of a sterndrive is very similar to that of an outboard ...and on a boat with an outboard mounted right on the transom, they'll have similar drafts. That said, most people mount an outboard on some type of bracket. The water in the wake rises behind the boat, hence the higher mounting of outboards on brackets. The further back the outboard is due to the bracket length, the higher you'd mount it so that the cav plate is running near the surface of the water. So, the short answer is 'it depends, but yeah, the typical outboard mount runs a little higher than a sterndrive'. The difference won't be more than an inch or two at most though ...not worth worrying about. The bigger differences between the 2 power options are initial cost (30% more for a sterndrive), gas mileage (50% higher miles per gallon with a sterndrive), and higher maintenance costs (over time) for sterndrives if they are left in brackish or salty water all the time. The higher mpg sounds good, but consider that's also diesel compared to gasoline in most cases, and diesel costs more, so this is a range issue more than a cost savings issue.
I like sterndrives if you can afford their initial cost, your boat is a trailer sailer (not kept in the water 24/7), and you want extended range for the boat. Most people are best off with a good efficient outboard such as a modern 4-stroke or a TLDI 2-stroke, and carrying extra gas in a few box tanks when you need it (or work some under-the-settee box tanks or under-the-sheer saddle tanks into your build). Lots of good options on tankage out there...