Zach,
I'm going to say "no shoulder plane" (I'll explain below). But as far as shoulder planes, I like the LV most because of the adjustment screws and ergonomics. The LN is basically a clone of a Stanley. Great plane but adjusting the blade can be a pitb.
Explanation: They are called shoulder planes for a reason and I try my use for whats is intended for: shoulders -- not the faces of a tenon. But, we all do it anyway. The reason is that it is quite easy to create a sloping tenon if you don't hold it perfectly 90° to the shoulder.
IME the best method on large tenons like yours is a router plane. You can install an extended base. This ensures a perfectly flat tenon that is perfectly parallel to the face of the board - absolutely critical the longer the tenon is.
I will also use a rabbet block plane on large tenons.
BTW, both the rabbet block plane and shoulder plane are extremely useful tools I highly recommend them to all hand tools users.