One of my favorite ways to show the similarities of two Presidents is to show similarities in states in voting for one or the other. It is hardly surprising that Hoover in 1928 and Eisenhower in 1952 should win mostly the same states. Hoover promised peace and prosperity, and got only peace right; Ike could deliver. What is truly eerie is when the two presidents are from opposite Parties, as between Eisenhower and Obama. Partisan affiliations have changed dramatically since the 1950s, but while much of the Democratic vote of the 1950s has since gone Republican and vice-versa, the similarities between Eisenhower and Obama present themselves in an odd way.
It is telling that Eisenhower won three states (Massachusetts, Minnesota, and Rhode Island) that no Republican nominee has ever won together since 1924 -- and Ike did it twice. I'm guessing that Ike did best in the states with the highest levels of formal education -- which is much the same in the 2010s as in the 1950s. Eisenhower and Obama both won Virginia after long dry spells for Republican Presidential nominees in that state for their respective Parties' nominees for President.
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When all is said and done, I think that the Obama and Eisenhower Presidencies are going to look like good analogues. Both Presidents are chilly rationalists. Both are practically scandal-free administrations. Both started with a troublesome war that both found their way out of. Neither did much to 'grow' the strength of their Parties in either House of Congress. To compare ISIS to Fidel Castro is completely unfair to Fidel Castro, a gentleman by contrast to ISIS.
The definitive moderate Republican may have been Dwight Eisenhower, and I have heard plenty of Democrats praise the Eisenhower Presidency. He went along with Supreme Court rulings that outlawed segregationist practices, stayed clear of the McCarthy bandwagon, and let McCarthy implode.
You can ignore the numbers which indicate electoral votes from 2012.
gray -- did not vote in 1952 or 1956
white -- Eisenhower twice, Obama twice
deep blue -- Republican all four elections
light blue -- Republican all but 2012 (I assume that greater Omaha went for Ike twice)
light green -- Eisenhower once, Stevenson once, Obama never
dark green -- Stevenson twice, Obama never
pink -- Stevenson twice, Obama once
No state voted Democratic all four times, so no state is in deep red.