Been a while since I've looked at naruto to be honest, but I suppose I have a predilection to playing Uchiha or a Hyuga, however this is with full awareness of that both ocular jutsu have their strengths especially on a Genin when not taken care of. Byakugon at least stayed at a relative strength level as seen in Shippuden to where even super fast Lee couldn't beat Neji since it's not just 360 view but also that would mean Neji could still react to and fight off Lee in a spar. Where as with what happens to Sharingan.... shippuden made it a bit ridiculous and I dislike it from that forward. I like the base Naruto level of coolness and ability it gave with learning etc but I also like to remember that it's not supposed to be common for Uchiha to acquire originally even themselves, even without Sharingan I like the Uchiha has a clan I suppose from the firejutsu available and their place in the village before they were all killed.
We never did get to see Sharingan vs Byakugon in a real good sense, kinda sad since I think that would have been an interesting fight especially if it was like Sasuke vs Neji in the chuunin exams. That would have given us a far better relative strength of what were relatively normal Kekkai Genkai in terms of strength at the time.
I think when I was in one before I ran like a Sarutobi once which is pretty much a 'normal' clan without much special.
In my opinion, Sharingan and Byakugan are both at the relatively same level. Things change greatly when we talk about the Mangekyo Sharingan, which is a much stronger kekkei genkai, usually.
Think of the Sharingan as a more energy/chakra based dojutsu: It allows the Uchiha to utilize genjutsu by making eye contact, to copy and understand ninjutsu used by others, to predict certain movements and such.
The Byakugan is a more precise, physical dojutsu: It allows the Hyuga to see a LONG distance away, see the chakra pathways with such a precision they can strike specific points to disabre them with their Gentle Fist and such.
At least that's how I personally see it. If we do get into the story, chances are I'm going with an Uchiha as well because I'm a sucker for them red eyes.