I’m biased because I’ve had Sun/M off for forever and so for me the grass is greener - I’d like to get F/Sat. Not gonna happen for at least five years, though. So I make do. There are definite advantages to havving a weekday off and I can think of both plusses and muses for either day.
The biggest minus for me is I work evenings, which means I lose Friday night entirely. Which definitely can crimp socializing - fewer people want to do things on Sunday or Monday night ;).
Alice: congrats on the new job!!!
I know this is now moot but answering the OP (and thinking positive: the new job may get flex time at some point too) …
I’ve worked pretty much every pattern you can imagine including the pattern where there is no pattern. **Master Blaster **just above pretty well nailed it.
Look at your work & your coworkers and decide which day off makes your work life easiest.
e.g. Avoiding Manic Monday and working Casual Friday might be best in your world. OTOH, avoiding the every Friday Afternoon 4pm Crisis and sitting through the useless, boring, but really easy Monday of Interminable Meetings might be better.
I mostly prefer to work weekends and have some weekdays off. I live and work in a world with little road traffic and uncrowded stores and restaurants. My neighbors with traditional schedules don’t.
All else equal, Fridays have more other folks off than Mondays do. So if minimum crowding for retail, recreation, etc. is your main goal, be off Mondays. OTOH, almost nothing anywhere is closed on Fridays whereas in some areas many things are closed on Mondays. Only you know your local situation.
As **Tamerlane **says, you ned to cultivate a set of friends with similar schedules. And the wierder yours is, the weirder theirs (and they) have to be to match. As between being able to stay out late and play on Thu night or Sun night I’d bet you’d get more takers for Thu night.
I messed up and chose Fridays, but I actually prefer Mondays, if, like most places I’ve worked, there’s a casual Friday option.
But I’m not a big fan of 4/10 workweeks. If that’s what we’re talking about here, I’d rather work a regular M-F schedule.
All I can say about this one is that whatever you hate about Monday will become a new Tuesday problem. Whatever you hate about Friday will become a new Thursday problem. No net difference, whatever you do. “Wherever you go, there you are”. I voted “don’t care”. I didn’t read the thread, because this is likely to have already have been said several times. I’m just "me too"ing it.
Now I’m going to read the OP’s thread… Might be interesting.
This is my reasoning as well. I wouldn’t really care which one, as long as I got a 3 day weekend instead of a 2 day one. AT the same pay of course. 
Fridays, definitely. If you’re in the US: a disproportionate number of Federal holidays are on Mondays (Presidents’ Day, MLK Day, Labor Day) - on those weeks, you get a 3-day work week (woohoo).
Plus - if you’ve got Mondays off, then on Monday you’ll be feeling depressed that the work week is about to begin. Same as you do now on Sundays.
when I was off on Fridays I just started the weekend earlier. when I was off on Mondays I was Taking Care of Business…
Probably not as much as you think.
Yes, if they dread going to work, period, then Tuesday will feel like Monday in that respect.
But in most work situations you’re not totally alone, totally responsible for the content of your day. If everybody else makes Mondays crazy & Tuesdays calm, then staying home Monday avoids *their *craziness. Likewise, if Fridays are everybody goof off from noon to close, odds are you won’t be able to get away with doing the same thing on Thursday just because you won’t be there on Friday.
I switched to an alternating 5/4/9 schedule last year and had my choice of Mondays or Fridays. I chose Mondays and love it. If I want to go out and get things done on Mondays, nothing is busy. I feel like I can get more done on a Monday, or if I want to lay around and just relax, I can do that too. Starting the week on Tuesday is pretty nice too.
One thing I’ve also noticed is that Thursday has become the new Friday in a lot of places. I think most people have Fridays off, or take their vacation days on Fridays, and it really seems like its the weekend in many places (particularly in the summer time). I’m not a big fan of crowds, that might explain my passion to have Mondays off vs Fridays.
I’d rather be off Fridays. On my days off, I like to shop at small restaurants and hole-in-the-wall shops. Virtually all those places are closed on Mondays. And good luck if you need to get a haircut on Mondays. Friday everything you could want is open.
I voted Monday because I feel like I would get more errands done. If it was Friday, the first day of my weekend, I’d sleep in and fart around and about the time I wanted to run my errands, people would be home from work and I’d lose any advantages of being home during a weekday. But, it would be easier professionally to be home on Fridays, big meetings and such often happen early in the week.