There are two ways of doing any thing in this life;
a. one follows the guidance of Islaam which is sent from Allaah.
b. one follows his own desires and do what feels better for his heart.
If we have to take the first option then a Sunni person whether a man or woman should not marry a Shi'ah.
The differences between the Ahl al-Sunnah (Sunnis) and the Shi'ah are too big and fundamental. It is not correct to say we are all Muslims and division should not occur, because we are Muslim by our beliefs if belief becomes corrupt to the extent of denying the validity of Quraan and attributes of Allaah then this is disbelief.
Although the Shi'ah call themselves Muslims, many of them in fact leave the fold of Islaam by:
1. Their beliefs, such as believing that some part of the Qur'an has been removed by some people, or that prophethood was meant for someone other than the Messenger of Allaah and by mistake it ended up on him, or the Imams being more knowledgeable than the prophets, and their exaggeration about their imaams and worshiping them, and giving them precedence over the Prophets and angels; They also believe in hypocrisy (as a tenet of faith) and call it taqiyyah (dissimulation) so that when there is a need of taking some benefit they can hide their actual belief, and they believe in al-badaa' (the notion that Allaah "changes His mind"), al-raj'ah (the Return, i.e., the raising of the dead to life again for some time in the same form as they were before) and absolute infallibility of their imams.
2. Their actions, such as making additions in the Shahaadatayn or praying in a manner not prescribed in Islaam. they prostrate on a handful of clay or leaf from Karbala.they go on pilgrimages to mashhads (shrines) and graves, where they do all kinds of actions of shirk, associating others in worship with Allaah. They condemn most of the Sahaabah (may Allaah be pleased with them) use abusive language for them and consider them disbelievers.
There are too many other beliefs and actions to mention here. They have a spectrum of people, the mildest of whom are innovators and the worst have no limits. Also see the attachment.
A muslim must seek a pious spouse because a pious spouse will help him/her to achieve paradise while a deviant one may drag him/her into hellfire.
And Allah the Most Knowledgeable knows what is best and most correct.
May Allaah help and guide us to do all that He is pleased with and his Peace and blessings be upon His last Prophet Muhammad.