I'm going to focus solely on the issue of mechanical disc versus rim brakes.
All else equal, I would prefer rim brakes to mechanical disc. Mechanical disc brakes (and the hubs, and possibly the frame as well due to increased manufacturing complexity) are more expensive than rim brakes. This means that if the bikes have the same price, then the one with disc brakes would have more compromises elsewhere in the spec (on average).
In my (admittedly limited and second hand) experience, mechanical disc brakes have relatively poor stopping power out of the box - one bike I helped someone buy stopped more poorly than my bike with good rim brakes. Mechanical disc brakes need good compressionless brake housing to work well, which entry level bikes don't come spec with. Also, they need more frequent adjustment than hydraulic disc brakes. You have to adjust the position of both the inboard and outboard brake pads as the pads wear down. With rim brakes, you just turn one barrel adjuster. With hydraulic disc, the brakes self-adjust.
For cheap rim brakes, the compromise is that the brake pads are often poor quality. This is very easy to rectify. While we do state no product recommendations in the FAQ, we do break this rule to recommend Kool Stop brake pads, which I believe are available in the UK (it's a US-based company). If you feel your rim brakes don't brake adequately, have a store change the pads and holders first, or do it yourself.
If you get more interested in cycling and want a higher-spec bike, chances are that you'll later sell off the bicycle wholesale. It's almost always more cost-effective to upgrade the entire bike, rather than upgrading piecemeal. I would wager that mechanical disc brakes are no better than rim brakes of a similar price point. In contrast, on a much higher-end bicycle, hydraulic disc brakes do objectively have more stopping power (especially in the wet) than rim brakes, so in other contexts I would usually recommend hydraulic disc over rim brakes at a similar price point.
Terminology: you are looking at a bike with mechanical disc brakes. These brakes, as well as traditional rim brakes, are operated by a steel brake cable. In contrast, hydraulic disc brakes are operated by hydraulic fluid, e.g. mineral oil or DOT fluid as used in motor vehicles. One of the bikes you identified was equipped with Shimano Claris, its entry level road groupset. On Shimano, hydraulic disc starts with Tiagra, which is two levels up from Claris.