A 3-4 lift is much cheaper overall. Stock drive shafts work, in some cases stock brake lines even work. A 3-4" lift on an NT is good for 31-32" tires. Drop pitman arm, some longer shocks, and you are typically good to go.
An SOA you typically need at least a new front drive shaft (high angle), especially as you have QT so that shaft will always be spinning unless you have a part time kit. You may need to change the cross over pipe for the exhaust to clear the front drive shaft. Brake lines are a must, steering is a must (including at least one new or machined current knuckle for steering), longer shocks of course than a 4" lift. 31" tires look goofy, so you will spend more on tires. And then you will hate the gearing, so you will want to regear. And then an SOA on NT axles is not the most stable thing, so you may want wider or stronger axles to go with the larger tires.
But then, this tends to be how every Jeep project goes
I guess it comes down to want your end goals are. The SOA will ride nicer due to having stock height springs. You obviously have more clearances, and it will articulate better. But it does cost more.
The 3-4" lift is a day in the garage. An SOA is a lot more involved, and requires welding.