Every version of Shadowrun advances the setting timeline (usually 5-10 years), but that isn't what you're asking about.
Other than using the same dice and reusing a few of the attribute names and other terms, the systems are very different. Die pools are calculated differently, variable Target Numbers no longer exist, the Matrix became wireless in SR4, etc. There are too many differences to provide a bulleted list of the mechanical details - it would essentially need to cover the entire system.
As far as complexity goes, it is definitely much less complex. That's been an ongoing trend since SR3 - each subsequent edition has a lower base complexity. Obviously, each successive sourcebook within an edition increases the complexity, but no edition since SR3 has reached the same complexity of SR3.
If you're going to start fresh and looking for a less complex game, SR6 is probably the place to start. There isn't a pile of sourcebooks to add complexity (yet). It is also more readily available in dead-tree, for people who like that.
Shadowrun holds a special place for me (SR1 was actually the first RPG I spent my own money on as a ten-year-old), SR3 is my favorite version of the system and my favorite version of the setting. There are a lot of things that happened at the end of SR3's run that I don't particularly care for from a storytelling perspective. They tried too hard to update the setting to better reflect the modern world while maintaining their modified timeline at the same time; it felt very heavy handed.
The complexity of SR3 is a hard for a lot of people to take. When I run SR for anything but diehard SR veterans, I usually use SR4A (20th Anniversary Edition) for the rules but early SR3 for the timeline. I blend some of the technology backwards, to better reflect those advancements from the modern day, e.g. the wireless matrix is not a new thing (as it is in SR4's timeline), it comes after the first Crash, rather than the second (and I never run games in a timeline that gets that far).
Depending on how far back I plan to start, some things may be completely unavailable, too - Move-by-Wire and Biofeedback Filters are two pretty significant technological benchmarks. There's actually an entire adventure module about how the first true defense against Black ICE was created.
If you're willing to accept more complexity, but not as much as SR3, go with SR4A. There are plenty of sourcebooks to tailor your game with. It will be a bit harder to find those materials, though.
I honestly believe SR3 was the height of Shadowrun. Even the most crunchy sourcebooks had great setting information, typically in the form of running commentary at the bottom of each page from the in-universe online 'runner community, Shadowland. As in-character commentary, a lot of it could be lies or truth as the GM chose.
During the FASA years, there was a certain wit in the writing. I mean, who nukes the location of their own corporate headquarters?1 While some of the same people were involved in WizKids, it just wasn't the same. As time went on, I think the rules got less complicated (better, in many cases) as things transitioned from there to FanPro, but I think the backstory got weaker.
Catalyst Games didn't really improve things much. SR5 introduced some good concepts (I for one, liked Limits), but at the same time introduced some really out-there story elements. Cognitive Fragmentation Disorder was a real stretch; it seemed like they were trying to recreate the body/mind horror of Bug City or Renraku Shutdown, but fell flat.
Furthermore, from a layout and editing standpoint, Catalyst has done a poor job. There are whole passages in SR5 that are literal copy-pastes from SR4, that were not subsequently updated to match SR5's nomenclature. Likewise, there were sections they lifted to explain certain concepts, but did so incompletely - if they'd included a paragraph before or after, it would have made sense.
I've purchased and read SR6, but honestly have no plans to run it. I'll stick with SR4A.
1The "Cermak Nuke" in Bug City... FASA's offices were on Cermak Avenue in Chicago.