Airbus traditionally has more computerized, complex systems for pilots.
Not really, at least in complexity terms. Maybe this was true 20-25 years ago in the 737 NG vs the A320 family, but not today. Airbus does have a few more envelop limitations in its flight rules though.
But it was the somewhat dodgy aerodynamics of the 737 MAX - caused by the desire of the money ppl at corporate HQ to cram as many passangers in a modified 737 as possible for long haul - that caused the need for a sensor based automatic pilot override system, which some pilots didn't even know about, and which can clog up in bad weather, causing faulty data to make the 'plane change altitude when it shouldn't.
It was a centre of gravity issue as well, rather than just aerodynamics (centre of pressure).
Boeing put a larger engine on the 737 to complete with Airbus' decision to put a larger engine on the A320. As the 737's wing was lower off the ground, the larger engine had to be moved up and forwards to accommodate the new engine.
Airbus customers transitioning to A320s with the new engines only needed computer-based type difference training for their pilots. Meaning they don't need to pull pilots out of rotation for a day or two to complete (expensive) simulator or practical training to maintain their type certification for the 'new' aircraft.
Boeing was under pressure to deliver the same for the 737 MAX. The problem was that the new engines (and new nacelles and new landing gear needed to accommodate them) created a nose pitching up movement in the aircraft at slow speeds as it heads towards a stall and/or as engine power is added. This is the opposite of what you want.
So they put in some new features (known as MCAS) into the flight control software to automatically pitch the nose down and make it fly like the older 737 - thus not needing more than computer-based type difference training for pilots and matching what Airbus could offer.
The problem came when the airspeed sensor was blocked/failed. This told the MCAS system the aircraft was stalling - even when it wasn't - and ordered the flight control software to pitch the nose down.
End result, two crashed 737 MAX aircraft.
The basic workhorse 737 design is excellent and safe; it's what the moneybags ppl forced it to do by making modifications that stretched its aerodynamics to the limit, that is behind the present troubles.
Ehhhh... The basic 737 structural design (talking about the 737 NG here) is fine, but its not really anything more than a interim quick/dirty response to introduction of the A320 family (which basically blew the 737 CL away in terms of technology and capabilities). Boeing has been looking at doing a clean paper narrowbody for at least 25 years, but one thing or another has stayed their hand. The 737 MAX is essentially an interim update to an interim update.
As for the 737's safety - yes its as safe as any Western manufactured large commercial airliner. However, this 737 MAX situation is not unique - the 737 CL suffered multiple fatal crashes (officially two, more realistically three and possibly as many as five) in the early 1990s due to rudder issues.