we have all 4 of these in our family. I will say that I have had experiences with many small breed dogs & usually more than 1 from the same breed family and can honestly say that while there are some breed specific personality traits, there is also a whole lot of diversity!
This is a long post, but you asked, and I have a lot to share!
My parents have a Pom. This is their 6th one. She is by far the most difficult they've had. I actually believe she may be a bit "off" as she is SO different from the other Poms they've owned. I tell my folks she is not really a dog, but a goat in dog disguise. This dog eats anything & everything - including metal & glass. She has torn up so much of their stuff it's sad. They love her, though. She is a lovable dog. Just almost impossible to train to do anything! That said, their other Poms were very smart, easily trained, loving animals. One trait I've seen all Poms share - hyperactivity.
Shih-tzu - I have a 6 year old shih tzu, Rufus. He is standard size for a Shih Tzu - about 12 lbs. - most of which is fur! He is a funny, sweet, loving, fiercely loyal companion. He didn't get the memo that he was supposed to be a lap dog, though. He loves to exercise, run & chase the ball. He is somewhat shy of new people, but not at all aggressive. He doesn't like young children much, but that is because his exposure has only been to kids who like to lunge at him & pull his hair. Pros - sweet, loving, loyal, playful, adorable, gets along with other animals (even loves to play with cats), easily trained & super smart. Cons - grooming time. But I got him because he's hypoallergenic with hair, not fur, so I keep him in a puppy cut. I spend about 30 minutes a day combing his hair, cleaning his eyes (flat faced dogs need close attention to their eyes to avoid injury), and just bonding with him. Psst - he doesn't have a clue he's a dog. So, don't tell, 'k?

Oh, yeah, and typical of his breed, he "talks." When he wants something, he will tell you. It's a riot.
Here's a pic from about a year ago:
My daughter has a miniature Yorkie. We had heard about the problems people experienced with Yorkies (or really any terrier breed), but did our research & found a really reputable breeder who took care to breed out certain personality traits & breed in desirable ones. We LOVE our little guy. He is super friendly, loves kids & other animals, super sweet & loving, a real cuddlebug, and a bit of a diva. He actually came into a house of 4 dogs & established dominance within 5 minutes.

Tiny little guy requires regular (daily) brushing, regular (monthly) hair trims/grooming, and LOTS of attention. This dog is a constant companion & loves to snuggle. He is not yappy, does not chew anything other than his toys, and is potty trained. Pros: sweet, loving, steal your heart sweeties Cons: a bit harder to potty train than other breeds, but with effort & paying close attention to signals can be done!
Here are a few pics of my grandpuppy:
He likes to sit & watch while you get a bath. Quirky little guy:
And a pic of him getting in my DD's suitcase to say he wanted to go to Disney, too!:
As for Chi's, well I don't have alot of good to say about them. My husband does have one, Eechie (7 yrs old) that doesn't fit the usual mold of yappy, snippy, mean critter. He's actually pretty cool. But not trained well AT ALL. And obstinate. But he's friendly with people & other animals. All the other Chi's I've had contact with, however, have been awful, mean little dogs. But Eechie is an example of one that isn't, so I guess there are some out there. I don't have a picture, but he isn't typical there either - he's VERY overweight. He should weigh about 6 pounds, but comes in at 13! Yikes! He lives to eat. When he's not eating, he sleeps. lol
Good luck in your quest for a new doggie companion!