Is using a drawknife better at carving vertically (I want to keep it smooth)? I have wide wood chisels but figure it would be easier and faster to use a drawknife.
While you could certainly do all the work with chisels, or with chisels and a spokeshave, if you have a fair amount of wood to remove a drawknife would be an excellent choice.
Drawknives excel at doing what drawknives excel at, and efficiently working a surface down while keeping it fairly smooth is one of those things.
Safety note: if you've never used one before please take care! When using a drawknife by necessity you cut towards yourself and injuries are not unheard of.
And what kind of drawknife is better... straight or curved, 5" or longer?
This is not something you can get a definitive answer to (here or elsewhere).
Obviously different people will each have their own opinions about what type of any tool is good/better/best and a great deal of it is merely personal preference. You'll find your own, based on your stature, hand size etc., the type of wood you're working (green versus dry or partially dry, as well as the species) and the nature of the work you're doing.
Just in relation to size, the knives I've seen most commonly in actual use suggests that 5" is broadly considered too small to be a good general-purpose version of the tool. Larger versions are obviously capable of the initial hogging-off work from a sizeable log but the same tool can be used with finesse to take off slivers from a narrow stave (around the scale that you'd otherwise remove with a spokeshave, although requiring more control).
Buying
If you're not in the market for an old one best of luck in your search for a decent new one! Almost every drawknife user I know of or know personally uses mostly or entirely vintage or antique knives.
Part of this is simply because in some parts of the world vintage knives (which are almost always good to excellent) can be found relatively inexpensively — a quarter of the price of a new one, sometimes much less e.g. if in need of replacement handles. But it's also that it's not easy to prep some new ones.
Sharpening
Regardless of whether you buy new or old, be careful when honing it. With many sharpening methods for these tools your fingers come perilously close to the cutting edge and it's getting keener and keener as you progress.....