Here's what I know of Alexei:
1) Much like Bloody Mary, he never forgave his father for divorcing his mother
2) He was raised by "new" men, but he was very much influenced by the "old" ways and the boyars
3) He was disliked by his father, particularly after Marta Skavronskaia came on the scene and bore him sons - Pavel (1704-1707), Pyotr (175-1707), Pyotr (1715-1719), Pavel (1717-1717), Pyotr (1719-1723)
4) He (Alexei) didn't like his wife, Sophie of Brunswick.
5) He might not have liked her, but he had two children by her: Natalia (1714-1728) and Pyotr II (1715-1730)
6) He fwas religious, superstitious and reactionary, but with no interest in politics or the military
7) He fled Russia in 1717, first to Vienna, then to Naples
8) On his return to Russia, he was subjected to a trial that was more for show than anything else; he made a confession of guilt and begged to be forgiven; pardon was granted on condition that he renounce all rights to the throne (in favor of his half-brother, not his son) and make a full and detailed confession naming all his accomplices
9) Peter nailed his coffin shut by claiming Alexei had omitted one detail from his confession: he neglected to mention that his letter from Vienna had begged protection from the Russian nobility and clergy. Even his mistress, Afrosyna, testified to this
10) He died at the Petropavlovskaia fortress in St Petersburg, following a visit from his father
All in all, Alexei and Bloody Mary have a lot in common - both were born of their father's first marriage; both wanted to turn the clock back; both had difficult relationships with their father; both had to accept a stepmother they didn't want (the only difference being that Anne Boleyn was more educated, but less fertile than Marta Skavronskaia); both were strongly religious, the list goes on.
But IMHO Alexei wouldve been a terror to the "new" Russians much the same as Mary was to Protestant Englishmen. Alexei was weak, hesitant and impressionable - not good qualities for an autocrat - Nikolai II was the same in many ways, and it cost him his crown, his family and his life, Alexei might have tread the same path.