Why is second season's young William is so different than one from the first season

About The Timeline and Backstory

First, the Westworld Park and the Hosts were not originally owned by Delos Corp. It was owned by Arnold Weber's and Robert Ford's company, Argos Initiative.

The season one backstory about Logan, a Delos EVP introducing William to park, where wealthy people like Logan can go to play, was not about a Delos investment at first, but rather William was was joining the Delos family by marrying Logan's sister, Juliet. Logan then saw Westworld as a rights of passage to William's manhood to prove he deserved to become apart of this elite family.

1.10 The Bicameral Man - Transcript:

LOGAN: I told you this place would show you who you really are. You pretend to be this weak, moralizing little asshole, but, really, you're a fucking piece of work.

WILLIAM: This place is remarkable. And I'm gonna make sure that our company substantially increases our holdings on the park.'Cause this place is the future.

LOGAN: Our our company, huh? Our company? My. Delos is my company, you piece of shit!

WILLIAM: I think your father's gonna need someone a little more stable to take over. You're reckless, Logan. Impetuous.

After having his heart broken in the park, William surpasses Logan's expectations to the point where William begins to see potential in what he believes (his beliefs are constantly contested) Westworld really is. In season two we learn how he was able to take over the family business and convince James Delos (Logan's and Juliet's father) to buy the park.

2.01 Reunion

James Delos is first seen visiting Sweetwater early in the the park's history. With the Hosts, including Dolores Abernathy and Teddy Flood frozen around them, James and William have a conversation about the potential of the park. William tells him that if James can't see the potential for data-mining of the guests, then he is not as good a businessman as he has heard. James likes William's courage at challenging him, and invites him to tell him what kind of ideas he has in mind.

Later, James is at his retirement party, having seemingly passed over Logan for control of the company in favor of William. James mentions that he does not have much time left and coughs repeatedly, indicating that he is ill. http://westworld.wikia.com/wiki/James_Delos

Note: The highlight passage about "data-mining" the guests was also restated as the point of Westworld by another character in episode 2.07.

In season 1, young William changed. He started off being timid and scared, but towards the end of the season, he turned the tables on Logan. In fact, William tied up a naked Logan and sent him on horseback off into the wilderness. He became, as you describe, cold and ruthless. Once he recognized the business opportunity of Westworld, which has been explored in season 2, then he could easily become the cold, ruthless businessman that we see.