Other than the obvious where DJ has a date and OP does not, the centre links of the DJ bracelets are all polished and DJ has polished case too.
The oyster bracelet with shiny center links is known to be a scratch magnet, avoid it and buy OP36 or DJ36 with jubilee if you can't live with scratches.
DJ is just a more blingy/shiny watch compared to OP. OP is more of a tool watch/everyday watch which wouldn't attract much attention while DJ just attracts a ton of attention by being so shiny.
My DJ36 with fluted bezel and jubilee got the most attention, even more than something like a hulk. While my explorer 1 got me the least amount of attention when I was wearing it.
I think that the OP/explorer 1 is just so good at being a subtle yet high quality watch that slips under the radar, nobody would know you had a Rolex unless they had a closer look. It's just nicer as a daily watch, and I prefer it's looks, but I just find it hard to live without a date function.
DJ is also a good option as a daily wear but it has more bling. I usually just wear mine with jeans/shorts and a t-shirt. It's totally fine unlike what others say online, but it definitely suits formal outfits more than casual ones.
Edit: something that bugs me with polished finishing on watches are the fingerprints and smudges that your fingers leave behind when you touch the watch.