Odd brake noises

I have an '07 Honda Civic LX. Unlike the EX, it has drum brakes at the rear instead of discs all around. When the brakes aren’t fully warm, they seem to make a lot of noise. It’s hard to describe: it’s sort of a rubbing noise, but at very low wheel rotation speed it almost sounds like liquid sloshing around. It takes more than just a couple of stops for the noise to go away.

I’m also not thrilled with the pedal feel as compared to my wife’s EX. There’s fairly long travel before you get much braking action, and the braking itself is fairly abrupt.

Does it sound like anything’s wrong?

You need to pull the drums off and check the wheel bearings.

The axle shaft may not show much play as it is supported by the brake pads, so pull the drums and take a look.

Do the rear drums get hot on just a short trip around the block without using the brakes ? They might be dragging for some reason.

While the drums are off and you’re doing the inspection, see how sharp the edges are on the shoes. If they’re really sharp, then file or sand the edges just a little. (Don’t breathe the dust) Do it outside or use a fan. Sometimes the sharp edges dig in the drums and cause the rubbing noise you describe and sometimes the same sharp edges will cause squealing brakes. I always bevel the edges of all the brakes I inspect or replace.
And as Curtis suggests, gingerly and carefully see if they’re heating up.
Check the edges of the drums for a worn ridge too. If you have a ridge, it might be a good idea to have them turned and put back on and adjusted. If you take them in yourself, it’ll cost about $10.00 apiece to have them turned and trued which should improve the lack of braking action.