It is a complicated question, and frankly not one that can be answered well at low tech for many reasons, not least of which is that low-tech fighters are usually quite poor in capability.
In this case you have your answer just from looking at the maint life and repair requirements. The military engine carrier will blow up in only a few months after leaving orbit. The culprit is of course that massive jump drive which because it is so expensive has a ridiculous repair requirement. You can also see that the BP cost is over 5x higher because of this.
However, as tech advances you can start to downsize your jump drives and the costs will drop significantly, at the same time the higher-tech engines and other components become more expensive so the importance of the jump drive will drop off over time. At some point it becomes feasible to build large carriers with military engines and jump them from place to place without crippling your entire shipbuilding or maintenance industry.
Even so, this raises an important point which is that even a higher-tech jump drive, regardless of naval or commercial, takes up a lot of space that should be going towards mission payload - hangar space, magazines, fuel, MSP, long-range sensors to identify targets, and whatever else you like to put on your carriers. It is almost certainly going to be a more effective approach to use a dedicated jump ship to escort your carriers, particularly since you only need a couple of them to adequately support your entire navy since carriers should never be involved in a jump point assault. The downside, at least for military engines, is that you will have to tie up a shipyard to make these, but you can just build a few and then retool to something else, and they will probably remain useful for a long time if you keep them out of combat. Another alternative is to rely on stabilized jump points, which limits the ability of your carrier fleets to prosecute an offensive - but not as much as you would think, particularly since most NPRs stabilize their own JP networks so you really only need to make 1-2 connections before invading.
As an aside, it is important with carriers to still consider the necessary speed to operate safely. Even at NPE tech, a carrier traveling at 1,000 km/s is extremely vulnerable to being chased down by an enemy fleet, especially if the fighter strike fails to kill everything or the enemy manages to surprise you. Generally, reasonable fleet speeds can be found at a given tech level from having 30% to 40% of the ship tonnage made up from 1.0x (no boost) engines - at NPE tech this will give speeds in a range of 2400 to 3200 km/s. For a carrier this can mean that you need lower-boost engines but larger to maintain a reasonable speed, which will have the added bonus of excellent fuel efficiency leaving more in reserve for the fighters. This means that to use commercial engines will likely require you to have over half your displacement dedicated to engines which may be extreme unless you have the massive shipyards to construct such a ship. Otherwise, military engines will prove easier to build and deploy in the field until you have the required infrastructure.