Religion most likely. At the time of Henry VIII's death I believe the Stuarts were still Catholic, whereas Mary Tudor's children by her second husband, the Duke of Suffolk, were all stunch Protestants.
That seems the most likely reason, and yes the two separates lines were both strongly divided by religion. Thanks.
Religion (along with the Duke of Northumberland's desire to stay in power) was the reason they tried to bypass Mary with the Grey line after Little Eddie's death. Didn't work well.
Interestingly Lady Catherine Grey, poor Jane's sister, was initially considered Mary's heir in place of Elizabeth, which didn't work too (although not so dramatic).