I did a few searches about these timers, but I couldn't really find anything directly comparing the two
That was attempted a few years ago. The resulting religious wars and hissy fits were enough to cause Sean, the proprietor of APUG, to ban product comparison posts in perpetuity and delete the whole wretched mess.
You cant find any direct comparison on APUG as there isnt one.
That said...
I think this is essentially the difference: The Stop Clock seems to have evolved from a print makers concerns and the DA from an engineering/scientific approach to the same issues.
They obviously both evolved from a print makers concerns - just different print makers. But in all it is a pretty fair statement.
At the system level the DA system uses a seperate meter and timer, while the RH Designs units integrate the timer and meter. In keeping with its name (not), the Darkroom Automation system has far less automation than the RH unit. On the other hand, the DA system gives greater control in placing print tones where you want them and allows precise control of midtones and midtone contrast; obviously this takes more time and effort than the RH approach of scanning for the brightest and darkest points and letting the timer pick the paper grade and exposure. The metered RH products have a really slick zone-scale that shows where the timer thinks the currently metered spot will show up. With the DA system you have to consult a grey scale you make specifically for the paper you are using. Stick-shift or automatic transmission - take your pick.
RH Designs has many more variations available and provides control for split-grade heads and integrating probes for cold-light heads. DA doesnt.
The RH timer has keys dedicated to different functions. The DA timer has just the one menu key that steps you through the steps in making a print: base exposure, dodging, burning, progressive burning etc. Each push of the key takes you to the next step. In either system you press a key to go to the next step in making a print: with the RH it is a different key for each step; with the DA it is the same key.
The DAs display is simpler, with no indicator lights for various modes as the menu system doesnt need them. On the other hand the DAs display gets a bit cramped and cryptic when programming memories.
The DA timer has more memories, assuming you buy the model with memories.
If you live outside of the Americas the choice is simple: get the RH Designs timer as DA doesn't make an export model.
The major philosophical difference may seem a bit obscure but is important.
The RH timers set and display the base exposure in seconds, which are adjusted by fractional stop intervals. DAs parent firm, Cleveland Engineering Design, produced a graphic arts integrator/timer for the nuArc corporation in the late 80s/early 90s that worked on the same principle of decimal seconds adjusted in fractional stops.
The current DA darkroom timer takes the stop paradigm a step further and works entirely in stops. Some find this a bit quirky, but it turns out to be more intuitive once you let go of the concept of seconds and start thinking in terms of exposure. After all, it is exposure you want to control not seconds per se. For consistency all base exposures, dodges, burns, progressive burns, test strip intervals, adjustments are all displayed in uniform decimal stops - this is also a break with the tradition of 1/2, 1/3, 1/4 ... stops.
As a result the DA timer looks less like the timer you may be used to, but looks an awful lot like the EV number window on a Rollei or Hassy and the EV numbers on a light meter.
The DA timer works in conjunction with the DA enlarging meter. Most sales of the meter are to people who use it only as a densitometer - it will read negative density to 1/100th of a stop (0.003 OD). However measuring negative density in stops has great appeal as it makes it easy to relate field exposure readings in stops to negative density in stops to paper exposure in stops. It is easy to control local contrast with the negative contrast index in stops of scene luminance to stops of negative density and the paper contrast in stops of negative density (the same thing as stops of paper exposure) to stops of print luminance.
By working entirely in stops the DA system integrates seamlessly with the work of exposing and developing the negative. This makes it a natural for people who are Beyond the Beyond of the Zone System. And this is the importance of this seemingly obscure philosophical point.
... the wood casing on the DA timer looks really nice. I know this seems a bit silly ...
Thank you.
Appearance and materials choice in product design is not silly. The look and feel of an object contribute as much to the enjoyment of its use as its function.
Appearance does count - hard for any photographer to argue otherwise when practicing an art that is about nothing but appearances.