Well, as I'm in the middle of a tropical storm right now, I can answer this from immediate first-hand experience, LOL.
Large Longchamp Le Pliage tote in black. This bag is made for rain. I've been using it nonstop.
I also have a small navy Longchamp Neo, which has a crossbody strap - this would be the ballgame/theme park bag for when I don't need to carry as much.
I also have a couple of vintage LV bags that I bought specifically to take a bit of a beating as travel bags - the Saumur 35, and I also have a vintage Petit Noe that I'm willing to sling around (although not in inclement weather). And then there's LV Damier Ebene bags - I have a small crossbody (Favorite PM) that I've worn to Disney World, and I'm about to get a Neverfull in the same print. Canvas bags in this print don't worry me in sweaty or dirty situations at all.
For true grossness, though - pools, farms, camping, grubby child activities, rain - Longchamp all the way.
Note: I bought a pre-owned Balenciaga Day bag intending it to be a beater bag, but NO WAY. Once I got it and felt the soft pillowy leather, I vowed to be good to it. LOL. I've used it as a carry on bag for a few trips, but I wouldn't take it anywhere too "rugged."