Essentially, the main contrast between Ulysses' past and present is that, in his past, the king was a mighty warrior and adventurer, while, in his present, he is an aged statesman bored with his idle existence and unhappy with the companionship of his family and subjects. One of the major points of Tennyson's "Ulysses" is to describe this contrast, and it quickly becomes very clear that Ulysses glorifies his legendary past while regarding his present situation with distaste. For instance, take a look at how Ulysses describes his past exploits:

Much have I seen and known; cities of men 

And manners, climates, councils, governments, 

Myself not least, but honour'd of them all; 

And drunk delight of battle with my peers, 

Far on the ringing plains of windy Troy. (13-17)

It little profits that an idle king, 

By this still hearth, among these barren crags, 

Match'd with an aged wife, I mete and dole 

Unequal laws unto a savage race, 

That hoard, and sleep, and feed, and know not me. (1-5)