1. The Hairstyle
Think about Lum's hairstyle and then think about Inuyasha's hairstyle. Both have long hair with two skeins (or bunches) at the front and a peculiarity on either side at the top of the head. For Lum it's horns and for Inuyasha it's ears. Both these peculiarities are like the trademark feature that distinguishes them from the 'normal' race (a.k.a the human race). Takahashi-sensei seems to like this look a lot as she uses it again for Shampoo in Ranma 1/2. Instead of horns and ears, Shampoo has buns but like Lum and Inuyasha, she is different from the 'normal' race as she is Chinese as opposed to being Japanese. Although the buns of Shampoo do not seem to enjoy the same attention as the horns and the ears, they are the one feature that doesn't disappear no matter what kind of outfit she maybe wearing (even in cat form the ears are reminiscent of the buns). Lum will wear a hat or a wig to hide her horns whereas Inuyasha's ears disappear altogether in his human form but let's not get into Shampoo.
2. The Outsider
In UY, Lum is an extraterrestrial alien princess and in IY, Kagome is a modern day school girl. Both are outsiders to the 'normal' world (the 'normal' world being the planet Earth for UY and the Sengoku Jidai for IY). Both of these characters have travelled across worlds to fall in love.
Even within the 'normal' world both of the manga are brimming with outsiders of society, in other words, people who are part of the 'normal' world but stand in the fringe. In UY, Ataru is the biggest lecher in the world and also one of the most unlucky. Mendou is so filthy rich that he is set apart from his classmates. Cherry is one of a kind and the same goes for Sakura and her fiance.
In IY, you have the half demon, Inuyasha, Miroku with his curse and Kikyou in her undead state. I'm not sure where Sango stands. I'm sure that being a demon exterminator (and a female one at that) would set her apart from society but she was once part of a village of demon exterminators that seemed to be interacting well well the rest of the world.
3.The Love Triangle
Pretty obvious in IY. The major love triangle is between Inuyasha, Kagome and Kikyou. There are others as well like the one between Inuyasha, Kikyou and Naraku, and then the one between Kagome, Kouga and Inuyasha and so on, I'm sure you get my drift.
I guess it's harder to say that there is a love triangle in UY as Ataru seems to like every single pretty girl who comes along with the exception of Lum herself (but he does get jealous because of her) but I would say the triangle is between Lum, Ataru and Shinobu.
4. The Cute Little Brat
In both stories there is a cute, little brat who seems rather attached to the main female character and not so friendly with the male character. In UY we have Ten and Shippou takes on the role of cute brat in IY. Shippou's relationship with Inuyasha does seem to be a tad better than Ten's relationship with Ataru.
5. The Comical Monk
A monk seems to provide some comedy relief in the manga. Short, old and withered Cherry gets a kick out of annoying the hell out of Ataru while taller, younger and better looking Miroku, tragic and serious in his own right, provides a few laughs with his groping hands and immoral reasoning.
6. The Miko
Both stories have a miko. IY has more mikos than UY but Sakura does get some holy shrine maiden duty and demon exorcising in between her job as the school nurse at Ataru's high school and dating her fiance. Not so busy with their lives, Kaede and Kikyou spend more of their time exorcising and protecting the village from demons.
7. The Lecher
As if to make up for its lack of mikos, UY gets more than its fair share of lechers. Firstly we have the biggest lecher in the world, Ataru, then there's Mendou, more subtle but just as perverted. And let's not forget Ataru's classmates who shamelessly take photos of Lum and any other cute girl in the school (Takahashi put in a few of them in Ranma 1/2 as well).
IY just has to make do with Miroku being the only pervert thus far.
8. The Demons
The worlds of both stories are overrun by demons. It's more apparent in IY with Inuyasha being half demon and most of their enemies also part of the demon race. It's less obvious in UY but I dare say it's okay to equate demon with alien. I mean, Lum is supposedly an alien demon (as opposed to her friend, Benten, who is supposed to be a goddess). Then there's Oyuki, the Snow Woman, a demon according to any Japanese and the kindergarten kids from Outerspace who came on a carp-shaped space craft look suspiciously like the insignificant small-fry demons Inuyasha and Co. have had the pleasure of killing.
Well, that's all I can think of now, I want to sleep.