Brobeck's is indeed delightful, and the small diner ambiance gives it a homey feel that underscores the good vibes of great food. Their ham salad is to die for, by the way. The burnt ends, purt near. I highly recommend Brobeck's.
Joe's KC BBQ, formerly Oklahoma Joe's, is by far the most consistent BBQ quality & taste in all of Kansas City, across the entire menu. Believe the hype. Joe's KC is legitimately the BBQ king in KC. This is where I take my out-of-town guests, and they always wanna go back.
No one can touch Jack Stack's beans, however. They are the best in town, and it's not even close. Pretentious white linens aside, the rest ain't too shabby either. The environs are just a bit stuffy.
Some others worthy of your consideration: SLAP's in KCK (meat-tastic), the Woodyard in KCK (smoking artistry), Jon Russell's in Overland Park & KCMO, Johnny's in Olathe & Mission, and Guy & Mae's in Williamsburg (oh the ribs!) just south of metro KC on I-35.
I'm long overdue to visit LC's for the first time, and it's been too long since Rosedale for me to comment intelligently.
Gates & Arthur Bryant's are true to the roots of BBQ in this sense: they try to elevate otherwise unappetizing cuts of meat to the edge of palatable with a mask of smoke and sauce. One notch above hunger though they may be, you can do far better in KC in lots of places.