Diana's photos are most of the answer, I think --- it really depends, as christyg points out, more on the knitters skill and abilities than the specific colours, patterns, etc. Finishing, fit and tension are the key, I'd say, between looking 'homemade' vs 'handmade'. That said, as Diana also pointed out, finer fabrications almost always look more 'together', whereas you would have to have chosen the yarn quite carefully and be quite skilled to get similar results with a chunkier knit.
Personally, I wear a lot of handknitted garments --- both bought and homemade by my mom and dad, who respectively enjoy knitting and crochet as hobbies, and really love spending yarn time together over the winters.
With the latter (garments made by my folks), it can be hit and miss what I end up with. My mom's tension is always looser than average and with age, her patience and dexterity with complex patterns has eroded, so I try to steer her towards simpler, straighter silhouettes with flat knits. Often, I get lovely basic sweaters, gloves, socks, vests in colours of my choosing this way --- in MY size, rather than having to trawl through the readymade mess. But if I end up with a slightly misshapen or too loose sweater, i'll still be wearing it a lot I know --- just around the house rather than to go out, and since I work from home, that's no bad thing!
With my dad, he likes to surprise --- and sometimes his colour combinations are a bit out there for me! Good thing he prefers to do shawls and scarves more than shaped garments, because I can use what I'm scared to wear as a throw or similar
And then sometimes, I'll end up with an absolute beauty that I either wear into the ground and store up sentimentally; or so exquisite it's saved up for special occasions. (He's really very talented with lace and such.)
Guess what I'm saying, in short, is that as with ANY other kind of garment, whether you get a polished look or not depends on the quality of the construction and the vision of the creator... and finally on how it's worn --- not on whether it came off a machine or was handmade. (I live in India, where handmade textiles are still the norm more than the exception, and custom-tailored is still half of most people's wardrobes. Levels of polish vary widely across both sets.)
