Plunkitt was typical of politicians of the time as stated. The idea of "honest graft" is one that is used to explain the actions of those politicians and there unfair practices. It is their attempt to justify the actions of the wealthy and their ability to use advance information to their advantage. The railroad debate is one that was major at that point in time. Being the most profitable industry at the time, it was of major debate how best to tax and regulate the industry. Many government politicians were very connected to the railroad industry so reform was not an easy tax, Senator Hepburn had some good ideas on how to arrive at the maximum rate but passing legislation would be difficult. It really was an appeal to the House and he was optimistic of the bill hoping that it would help railroad regulation.
Roosevelt's "New Nationalism" was one that unlike that of most progressive's of the time wanted limited regulation on big business. He was a reformer but believed that major regulation on business would destroy it rather then promote growth and allow for competition as advocated by other progressives. He was for a panel of "experts" in the fields needing regulation therefore helping to regulate not necessarily oversee the businesses. Many progressives didn't like this limited reform even though they endorsed him as a candidate he wasn't what they thought even though he garnered much public opinion.
Woodrow Wilson's concept of the New Freedom is one that proposed to overly regulate big business and to not perhaps extend the concept of laissez-faire but to allow for more competition in the market place. This was at a threat to individual liberty and to give the government far more power in regulation then was current at the time. His theories were more to break monopolies and allow for almost a somewhat socialistic control of the businesses by the government.
Roosevelt and Wilson were contrasting in terms of the power they wanted to grant to the government to regulate business.