Ceej I would characterize it thusly.
Livottis is a really big Italian deli with fresh meats and produce.
Trader Joe's is a specialty grocery store with an emphasis on prepared foods.
They both charge higher prices than normal stores because the cater to smaller households and the tendency of people to be too busy to cook these days.
I would say that TJs has a bigger selection of frozen nukeable entrees, including some good Tex Mex, Indian, and Asian items. If you don't feel like making a chili releno from scratch, but want one as a side with a steak, this is useful.
Traders is also nothing like what it was when it started, which was more a retailer of odds and ends from Europe, and cheap wine, in California.
I think the reason TJs has been so successful in recent years is young professionals and retirees using it a lot.
I notice in Shrewsbury that Traders always seems to be filled with 30-60 year old females in yoga pants, and there is no yoga studio in that plaza. They outnumber males 3 to 1 in that store. Whereas Livottis is more balanced, with a lot of middle aged and older men stocking up on sandwiches deli and meats.
Don't know why, but that's just my observation.