You want neither.
Even a monster wedge still has a very sharp angle to the sides. This is great to shield men from bad weather while they sleep. The design was not meant for "living in" (imho) I own two wedges, and they just aren't meant for that.
A wall tent is great, but not all events like wall tents, and as I have often helped my physically challenged friends to set up their wall tents, they are slow to put up, and take a lot of hardware, and such..., and are not really meant for one guy to set up. These were the stereo typical "hunting camp tents", but there was and is a better design, for those wanting simplicity in transport and setting up.
You Want a Double Bell Wedge Tent, ..., This below is with the "awning door" which saves on not buying an awning, but allows folks to see into the tent so you have to squirrel away any modern stuff. Mine has a different door, and I use an awning too...,
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This door is better for privacy..., this is what I have
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This canopy is elaborate, and a plain canopy will work...
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Here is a plain canopy with a rounded door..
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Most of the above photos are on the smallest version of the tents. Mine came from Tentsmiths, but they are rather expensive these days. Panther Primitive sells them as "medieval tents" but they were used up into the ACW, and they are reasonably priced. I'd get the 12 x 20 size. I can put this up all by myself with one ridge pole and pairs of poles on the ends to maximize interior space. The trick is to configure the poles like this....
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Last but not least the shape makes for very very good resistance to windy storm weather, the bigger the walls on a walled tent the more "sails" you present to the wind, and ...,the double-bell tent is absolutely a correct tent for a historic event. I regularly use mine for camping for five or more days.
LD