I wear Birkenstocks most of the time. I have a couple pairs for inside and around the house, they are both Arizona - open toe, double strap, no heel strap.
Around and about, it's Milano (Arizona with a heel strap), or Tokio (Boston closed-toe with a heel strap, and yes, that's how it's spelled), which is what I wear on the bike. A strange thing I avoid - footwear you can't run in when you're out and about - emergencies happen, and the Arizona sandals fly off my feet pretty easily. Great for slipping into around the house, though. As for the clunkiest ones - the Tokio - walked many, many miles per day in those, all day, for weeks, and never experienced any foot fatigue, discomfort, anything like other shoes or sandals I've tried, and they barely show any wear.
I'm typically a size 12 in Adidas, and 11.5 in dress shoes, and a size EU44/US11 in Birkenstock. My feet are just in-between, not wide, not high arch, etc., so I typically wear the 'regular/wide', but have one Milano set in the 'narrow/medium' exclusively for cycling, presumably to avoid chain grease.
The synthetic ones I've owned have been surprisingly nice, as of course are the leather ones.
I just don't like to wear socks, and as far as the feel of slipping a Birkenstock on my foot, even to this day after first purchasing them forty years ago, well, it might be inappropriate for me to say how it good they feel on my feet in a post on this community. Wearing socks and shoes, to me, is like having a three piece suit and tie on my feet.
I've tried Keens, Bedrocks, Chacos, Tevas - all fine, just like the Birkenstocks a whole lot more. Plenty of good deals for basically brand new ones on eBay, and often some pretty darn good sales on the Birkenstock US website.
As always, they work for me, YMMV.