Choose which one is actually the better oil. Just because it's a narrower multi-grade doesn't automatically mean better quality. In many cases, it's the opposite to an extent. If you notice a 5W-40 has similar Noack and HTHS (relative to KV100) to the 15W-40 version, you're better off with the 5W-40. Such a case tends indicate the use of cheaper, lower quality base oils and VII in the 15W-40. Narrow multi-grades like 10W-30 and 15W-40 can be formulated cheaper and still meet the grade. Since the major brands are all in a race to the bottom (including Shell... see my avatar), they happily exploit the lower production cost. (with no corresponding drop in retail cost, of course)
While this is all true, there are some market pressures that restrain their ability to make the oils as cheap as possible. Oxidation resistance being a big one because there’s relentless pressure to extend OCIs with the cheapest possible oils.
So in terms of cost-per-unit-oxidation-resistance, the current crop of diesel spec oils blows away most other blends only because it’s prioritized so highly within the formulation budget.
There are some solid 15w-40s out there. My current favorite for gas engines would be Delvac 1300 Super in 15w-40. It’s a blend with an API SP rating along with about every diesel rating on earth.
Valvoline Premium Blue One Solution in 15w-40 is also a very good oil with API SN Plus in addition to all the diesel ratings. They have a full synthetic HD oil in 15w 40 that is API SN (not plus).
Delo 400 XLE SB is 15w-40 and rated API SN.
Delo 400 XSP 15w-40 is full synthetic and API SN+ rated.
All of the aforementioned oils from Mobil, Chevron, and Valvoline are robust, full-SAPS oils with HTHS over 4 and very good oxidation resistance with reasonable gasoline API Specs. For an older vehicle in Arizona, you’re not going to find a better oil off the shelf for the cheap prices these HD oils go for. The cost effectiveness comes from the massive quantities they produce since they’re used in commercial applications that often have huge oil capacities.
If you value higher HTHS and oxidation resistance, these oils are a great way to get that for reasonable prices. Conversely, it’s almost impossible to find an oil at wal mart with an HTHS over 4 that is NOT one of these diesel-rated oils unless you step up to a 50 grade. Your typical A3/B4 oils even in 40 grade are going to be in the 3.7-3.8 HTHS range.