Vanakkam,
On a side note, I think how the devotee perceive God is important. Imagine a western woman who is looking to set a foot into Hinduism, seeking a first contact with a deity, or aspect or God. What will she feel drawn to ? The beautiful, infinite Narayana, wearing princely clothes and a jeweled crown, or the mysterious Shiva, half-naked sitting strange guy, surrounded by snakes ?
I may say complete ********** here, but that's my though :
In the west, we grow up with all the fairytales and stories depicting an ideal man, ideal king, ideal husband, ideal prince, ideal God. Full of virtues, crowded, adorned with fine clothes and wielding weapons to protect, to save, looking at his subjects with a concerned eye for them. We all grow up with these stories, should it be from Disney or the local lore (in Europe, especially the germanic and english, celtic lore stories are very accessible and are still told to childrens.)
They all depict this perfect man/deity/prince as a couragous warrior, a king, a shining knight full of a certain concept of beauty. (bright face, concerned eyes, good clothes, reassuring smile, weapons, crown, etc...)
I think Sri Visnu, in his various forms mirror this view of the ideal ruler/husband/protector/brother/God, because he have the attributes that show it, he have to attitude of being welcoming, full of glory. Should it be open arms, should it be His relaxed face and protective mudra, or should it be the playful look of Sri Krisna... Sri Visnu is depicted as explicitly protective, looking AT the devotee, he is looking like the handsome, protective, divine apparition many people dream of.
What of ShivJi ? In a western mind, he looks way more like a spirit, the ghost, the trickster of the story, not like the charming prince. He doesn't look appealing, and not even accessible: He is either depicted with his family, as a loving husband (he is then, not "accessible"), or as the ermit, shut to the world, with his eyes turned internally (he is not directly looking at the devotee). Who would like a half naked, snake infested hermit as a prince ? After all, as the story goes, Daksha and many people were totally horrified and opposed to a princess (Sati) marrying such a wild man (Shiva) ! He isn't the sweet looking, richly adorned prince, with his sword high up to behead all that come to harm the devotee ! No, He is just sitting here. Shut to the world. Unattentive to the physical world around Him.
Is it unfair ? No. Not one is better than the other. They are two different approaches for the devotee.
One is the easiest to understand, to love. Sri Visnu is directed toward the world, He is fully awake, aware of what is going on. Sri Visnu is action, He is active, acting, directed toward accomplishing the goal.
The other is the most mysterious one. Directed toward the Soul, eyes shut to the physical world. Inviting the devotee to know Him, feel Him, with the eyes shut too... And the soul open. Shiva is inaction. He is not acting. He is simple in apparence, silent. It is not easy to know Shiva, to go past the reflexes of the first impression, to detach from clothes, features of a face, or whatever else the physical eye may be drawn to, seeking to KNOW someone, or something. Shiva is nothing, but immense potentiality, inviting the devotee to seek the peaceful bottom of the ocean of potentialities. While Sri Visnu is nothing, but immense action, inviting the devotee to ride the agitated waves of the world, to reach his hand.
Yeah so quit saying stupid stuff Jaya, straight on: why womens are more attracted to Sri Visnu than Shiva ?
Sri Visnu look accessible (as a king, husband, friend etc) active, protecting, and correspond better to the ideal king/prince charming western womens grow up with.
Shiva doesn't look accessible (married man with childrens, or inaccessible hermit) he is not clothed like a civilized man, and carry in his look and attitude more the concept of the wild man/spirit/ghost western womens grow up with.
Vaisnavism is more directed outward, like Sri Visnu: toward external actions and devotions, it looks more like a bright light straight path. While Saivism is viewed as a more "obscure" one. Not in the sense of being bad, but Saivism is somewhat more inward directed, it is working on oneself, within ourselves. It require to sit still, to learn to tame the mind, it is also a more esoteric, mystic path. Something not easily reachable, accessible, that require to let go of the world in a total different manner from what is taught in Vaisnavism in general.
This is what I think, just don't mind if you think this is total stupid stuff xD I am trying to think, since I personally didn't have to "choose" or anything. Shiva just came to me. And that's all.
It is funny to see, as a Saiva, how sometimes people (non hindu or non saiva) "see" Shiva: litterally as the "destructor", someone to fear, the savage. I came across some people like this "How can you worship such a savage, misogynic God ?". What, in the eye of someone that is not a devotee a Shiva, gives this person this look on Shiva ? I think it is the look of Him.
PLEASE NOTE: I am aware not everyone is the same and therefore, I am not attempting to generalize anything, should it be on God or womens or sects. Also, I am not into the "Visnu vs Shiva" fight, and I am NOT attempting to prove superiority of one above another. This is not the purpose of this post, so please don't take offense.