Basically it comes down to used oil analyses (UOA's). I'm not aware of any better real-world method of understanding how an oil performs than repeated, controlled UOA's. They can provide you with baseline information about fresh oil and tell you how that oil is holding up, how much of its additives are left, and what metals and other contaminants are building-up after X time.

Beliefs in loading flat-tappet engine with Zinc dialkyldithiophosphate (ZDDP/ZDP) are based on decades old information. Oils have advanced tremendously just in the last few years, and beliefs like this trace back decades. Because science literacy is in such a sad state especially in the US, a lot of builders and engineers (not all) behind crate engines and even aftermarket cams and other parts may not even have the skill to understand proper scientific publications and simply rely on information, myths, and obsolete practices that they acquired through unverified word-of-mouth or outdated tradition. Back to UOA's, if ZDP was as necessary in the flat-tappet 4.0 as so many people insist, products like Pennzoil conventional (aka Pennzoil yellow bottle/PYB) wouldn't produce UOA's with such little evidence of wear and such long-lasting oil life as they do--PYB has no where near the ZDP levels claimed necessary for a flat-tappet cam. While also not perfect, here is a nice article about the ZDP myth.
Another way people choose oil poorly is fundamental misunderstandings of viscosity. Example time:
Many make the mistake of thinking that a 5w30 is a thinner oil than a 10w30 and that they shouldn't use it. This is right and wrong. When COLD, yes, it is thinner, but that is a GOOD thing. A cold 5 is still thicker than a hot 30, and in an engine designed to run with a hot 30, a cold 5 isn't going to be any danger. The thinner when cold, the better actually. Start-up is the time when the most wear occurs on an engine, and one of the reasons why is that the cold oil is thick.

Some are also under the odd belief that the 4.0 "likes" thicker oil and insist on using Xw40 or even Xw50 oils. Xw40 oils have been shown to be neither better nor worse in the 4.0 than Xw30's. Xw50, however, is simply a poor choice and even if it does not damage the engine, it doesn't help anything and thicker oil always negatively impacts MPG.

This leads to another false belief of many--that higher oil pressure means better protection. This often leads to people using excessively thick oils in order to increase their oil pressure to a level they belief is desirable, and it is wrong. Oil pressure is neither directly nor indirectly related to the performance of your oil. Keep you oil pressure within the factory specs, and do not draw any other conclusions from what the pressure happens to be on oil X vs oil Y.

I could go on about each of these subjects and others, but the nutshell is that when you eliminate all the junk science, superstitions, obsolete information, misinformation, and logical fallacies and gather good, trustworthy, useful raw data about how oils go into a given engine and how they come out of it and how much of the various parts of the engine come with it (which can all be learned from good UOA's), you can get a pretty good idea of what oils will treat your engine well and which you might want to play it safe and avoid.

After all that, I find myself returning to three very different choices each with its own particular role in my eyes.

• Pennzoil yellow bottle 5w30
  (This is the oil that I am currently using.) It is cheap. It yields outstanding UOA's in the 4.0. Anything cheaper isn't much cheaper and isn't as good, and you can't get any better than it for simple 3-5k mile oil change interval (OCI), so there's no sense in wasting money on anything more. 10w30 is also fine, but 5w30 will last plenty long enough for a traditional OCI without sheering (the risk of conventional oils with a large difference between cold viscosity and hot viscosity ratings), so why not get the one that will flow a bit better when cold, right?
• Shell Rotella T6 5w40
  Also fantastic UOA's. Also incredibly affordable. Not as cheap as PYB, so why don't I ignore it? Well, one reason is that some people sadly won't be moved from their belief that they need a lot of ZDP, and T6 is a great oil that these people will accept. Personally, it remains on my list for when an engine is potentially dirty because T6 has a great detergent level for dissolving and suspending sludge and other contaminants. It also makes for a very resilient oil for heavier duties like lots of wheeling/towing and other hard work especially in hotter climates. It is also capable in lighter duty 4.0's of safely reaching extended OCI's of 7500 miles or more (always monitor the health of an oil with periodic UOA's to verify its ability to reach your extended OCI during your first attempt and periodic attempts following).
• Castrol Edge 0w30 Euro
  I specify the Belgian or German make of this oil because there was a North American formula that was completely different and undesirable once upon a time. It is a relatively expensive oil, so why would I ever consider this one after saying not to buy more expensive oils than necessary? Obviously it even qualifies at all because it does indeed yield fantastic UOA's from the 4.0. The niche it manages to find that ultimately lands it on my short list is that of the extended OCI king. This is an incredibly long-lasting oil that has been monitored my numerous users in extended OCI's and shown to be incredibly sheer-resistant and maintain great protection in many cases well beyond 7k mile OCI's. If a 10k mile OCI is desired, this is the oil to use. As mentioned above, use UOA's during your first attempt to verify that it is holding up and still protecting into your desired mileage just to be sure. At a 10k mile OCI (some have run this oil even longer, though I haven't seen such long OCI's with this oil in the 4.0 yet), that $8 pint of oil actually has comparable value to PYB and T6. The trick to such long OCI's is either making sure you change your oil filter at a traditional OCI or use an oil filter specifically designed for extended OCI's as there are some that have been appearing over the last few years that are designed to last this long.

I don't claim to know it all and am open to learning more about oil and happily change my stance as new information is assimilated, but junk science, myths, superstitions, and years-old forum threads/hearsay are all virtually valueless to me at this point. Real data collected in a controlled, scientific manner that is reproducible/verifiable is what I look for. My choices are based on my best understanding of the industry, its products, and the science involved combined with the most practical logic I can manage as a consumer, Jeep owner, and inherently biased being (anyone who says they are unbiased is a liar).

I think that sufficiently answers the question: "Which oil do you use in your 4.0, and why?"