Merrick was bought out by Purina in 2015, and it's not the same quality that it used to be. I used to buy their lamb lung treats for my dogs, and can tell a major difference now.
I'm not familiar with Wellness Core at all, but I know Mother Hubbard treats and they're a very good quality. Their dog food gets 5 stars, too:
Rachael Ray gets low marks because of the junk food filler:
Of course those are dog food ratings, but I couldn't find cat food ratings. So just consider that a general guide, with the assumption that quality would be the same.
The increased water could be what's making your friend's cats healthy, that's always a challenge! Or it could also be unrelated and just genetics, who knows? I had a Chihuahua that I gave the best foods, and my parents took her cousin and only fed her table scraps, Ol' Roy Walmart food, and my mom smoked around her. My dog lived to be 14, but their dog made it to 19!
The puking could be that she's allergic to a specific ingredient, or there could be a contamination (mold has been known to grow inside of bags). I would definitely not feed her something that makes her throw up!
I'm not sure I could afford a higher quality food due to cost
FWIW, the Chihuahua was my first pet as an adult, and I started out buying cheaper quality food like that. As I got older and learned the quality differences, though, I moved her over to Blue (which was a great brand, but has since gone way downhill). It was more expensive upfront, but I quickly learned that she was eating far less of it, so it lasted longer... and at the end of the month I was actually saving money!
Before Charlie (my kitty) passed and I moved Mojo (his brother) to soft food, I would buy a 15lb bag of Chicken Soup for the Cat Lover's Soul to feed 2 cats for $15, and the bag would last for 2 - 2 1/2 months.