The Gibson J-200 is one of my favorite acoustic guitars - while Gibson acoustics have not caught on like their electrics, the J-200 is one model almost everyone would agree is a killer guitar.
However - anyone who says 'they're pretty much the same" or similar has no clue what they're talking about, so let me try to lay it out for you. Epiphone used to be a USA-made brand of guitar that competed directly with Gibson. In 1957 they were purchased by the same parent company that owns Gibson, in order to eliminate the competition. I'll spare you the rest of the history (check it out on Wikipedia) but basically since 2002 practically all Epiphone guitars are built in a factory that Gibson opened in Qingdao, China. While that factory is not AS-guilty of the heinous child-labor sweatshop tactics of so many Chinese "knock-off" companies..conditions there are still not great by USA standards, and are totally different than workers would experience in a Gibson facility in the USA.
You asked about quality: The real Gibson J-200 is an heirloom quality, hand-built instrument... the Epiphone is a mass-produced plywood copy. You'll pay more for the CASE of a a real J-200 than you will for the Epiphone version of the guitar. Keeping in mind that a Gibson J-200 (not EJ - the "E" is for Epiphone) retails for around $4000 ($5000 list) and an Epiphone EJ-200 retails for around $200 (you could own TWENTY of them for the same money) - so you'd expect there to be some substantial differences.
Construction: Gibson J-200s are largely hand-built and adjusted by the luthiers working in Gibson's Montana and/or Nashville custom shops. They produce a fairly small number of guitars per year.
Epiphone EJ-200s are built almost entirely by mass production techniques and unskilled labor (in China - often CNC and other computer-robotic manufacturing is not used, because human labor is so plentiful. . you'll have 1000 people sitting there, each doing one small operation over and over - like a machine would do except without the actual machine. To be fair about this - Epiphone's plant is much more automated than many Chinese manufacturers. But bottom line, the EJ-200 is a mass-produced stamp-them-out-by-the-millions kind of guitar. There is simply no other comparison beyond the shape/size that you can make.
Wood: The Gibson uses solid AAA (best) Sitka spruce top and AAA USA Curly Maple for sides and back. The Epiphone uses a lesser-grade of spruce for the top and maple PLYWOOD sides and back.
Fit/Finish: J-200s are meticulously hand-finished... bindings, fret ends, etc. will be fine-tuned, polished, etc. as you would expect from a $4000 guitar. EJ-200 are pretty much all machine-finished - while not "bad" , again you wouldn't expect the same care from a $200 guitar.
Hardware: J-200s use real adjustable-tension Grover tuners, If you were to buy them separately ,they cost around $75 (almost half the price of the whole Epiphone guitar) for a set of 6. The EJ-200 uses made-in-china die-cast tuners that look like Grovers, but are nothing like them. They're not terrible - but again, you get what you pay for.
Both the Epiphone and the Gibson can be set up to be easy-to-play... I've played both and the playability of the Epiphone was really good right out of the box (literally - they come in a cardboard box) .
Bottom line - the Epiphone guitar is great for students, campfires, class trips, and playing live gigs where you wouldn't want to bang up your $4000 Gibson. They play and sound decent for the money. If it gets damaged it's not the end of the world. It's a good value.
OTOH, a 'real' J-200 is something special that you hold on to and pass down to your grandkids... like all "real" Gibsons, the best examples appreciate in value over time - you can find examples of vintage (pre-1980) J-200s going for $10-12,000 or even more today.
Hope that helps.