If both planes were ready at the same time, I too would say the PAF should go for the KAAN. Considering the PAF’s parallel need for a new engine for the JF-17, focusing on the J-31 for the time being, as at least a place holder for a 5th Gen jet makes sense. Infrastructure build for it could be used by another jet.
I don't think TAI Kaan would be ready, as in, achieve the full capability of a 5th gen, or 5.5 gen jet, anytime soon.
From several details it's clear that Turkey have yet to have a mature understanding and technical expertise for full Very Low Observable designs. The radome edge is jagged, yes, but it is simple isometric uniformly jagged regardless of the geometry change, unlike other stealth examples that focuses on jagged lines that deflects radio return to very specific angles. The rear fuselage transition to thrust nozzle is jagged, but the nozzle itself is not (yes, it is just purchased F110 strictly for constructing the demonstrators.) The IRST setup and the lack of EODAS makes the awareness level of the Kaan still remains in 4th gen category. Not a single airfoil have clipped tips, the transition between control surfaces seems a bit rough, a distinct lack of conforming antennas for communication, navigation, and utility can be spotted from the fuselage. This is no surprising, Turkey, to my knowledge, does not possess Radio Anechoic Chambers or Supersonic Wind Tunnels, which no doubt limits their ability to design high performance, stealthy platforms.
The airframe itself is very conservative. Serrated Caret Intake, ~37 degrees wing sweep angle, still favors high subsonic-transonic, relatively bare bones - I personally think it's more apt to describe the TAI Kaan still in the demonstrator phase rather than prototype phase, aka where the FC-31 first prototype was.
The J-31 is a relatively mature design with many revisions, but in my opinion, it needs side bays for instance, to carry PL-10 missiles.
Let's objectively view what exactly does PL-10 brings to the table. It offers WVR ability, ability to engage target will remaining radio silent, HOBS post merge, and engage very small RCS targets like drones or some missiles.
As missile and information technology develop, the boundaries between WVR and BVRAAMs have actually been blurred. The EODAS system offers 360 degrees awareness, and is able to provide firing solutions to both WVRs and BVRAAMs. Directional datalink allows for interim guidance after LOAL, and the potent AESA seeker of the missile itself is enough to acquire the target in WVR ranges. Yes, BVRAAMs may not sport as much agility in post merge scenarios, but merging with a bandit as a VLO fighter in of itself is a very rare occurrence.
In short, as a medium VLO platform like KF-21/F-35/J-31/35 is considered, having just a main ventral bay means less digging holes in your fuselage, meaning weight saved in structural strength, and higher internal volume for fuel - both are very important that, some sacrifices are very much warranted.