The Senate this week will host two of the most high-profile hearings of the 111th Congress. Yet the scene in the confirmation hearing for Supreme Court hopeful Elena Kagan is likely to be far different from that of Gen. David Petraeus to head U.S. operations in Afghanistan.

Petraeus and Kagan do have a few things in common: Both have gone through the Senate confirmation process before, both are expected to be approved, and for both, their hearings will act as a proxy for debates over the Obama administration’s domestic and international policies.

But that’s where the similarities end.

For Petraeus — who has made numerous trips to Capitol Hill in recent years and is well-regarded by both Democrats and Republicans — his confirmation hearing before the Armed Services Committee on Tuesday is largely a formality. President Barack Obama tapped Petraeus, currently head of U.S. Central Command, to take over Afghanistan operations last week after he relieved Gen. Stanley McChrystal of the post.

Armed Services Chairman Carl Levin (D-Mich.) last week called Petraeus “a solid choice to take over in Afghanistan. He provides strength and he provides continuity. Indeed, he was the architect of the counterinsurgency strategy. He literally wrote the book that set that strategy out.”

“I think it’ll go quickly,” Sen. Richard Burr (R-N.C.) predicted.

“I have great respect for him, and I imagine there won’t be any problems with his nomination,” said Sen. Saxby Chambliss (R-Ga.), who sits on the Armed Services Committee.

The toughest sell for Petraeus will not be about his nomination. Rather, it will be over Obama’s strategy in Afghanistan and his plans to begin withdrawing troops in July 2011.

Sen. Lindsey Graham, another Armed Services member, agreed, saying he would use this week’s hearings to probe Petraeus on what it will take to win the war in Afghanistan. “Obviously, I’m going to ask him about, does he have what he needs and this July 2011 withdrawal date, how does that play, what’s his understanding?” the South Carolina Republican said.

Even though Petraeus’ hearing may delve into weighty issues of war and peace, it’s unlikely to feature the partisan warfare of Kagan’s upcoming hearings to serve on the high court.

While Kagan, now solicitor general, has largely avoided controversy since being nominated to succeed Justice John Paul Stevens, Republicans plan to use the Judiciary Committee hearings to bring her legal and philosophical beliefs to light. In them, GOP Senators hope to paint Kagan as a political operative who would be an “activist” jurist.

Sen. Orrin Hatch warned Thursday that he has become increasingly concerned that Kagan is too liberal and said that he will attempt to “pin down” the nominee’s beliefs on the law.

“For most of her career, Ms. Kagan has endorsed, and has praised others who endorse, an activist judicial philosophy,” said the Utah Republican, who sits on Judiciary.

Wary of these charges, Kagan’s defenders are ready with their counter: Kagan is highly qualified, has an impeccable record and would rule with impartiality.

For instance, White House officials on Friday previewed their strategy for the hearings: “I think that one of the more striking features of what we have seen up to date has been the breadth of support that Elena Kagan … has received from Democrats and Republicans,” White House Counsel Bob Bauer said.

Bauer also said that despite GOP complaints about her relatively thin résumé, Kagan is highly qualified to be on the court.

Bauer hailed her work as a law clerk for then-Justice Thurgood Marshall and as the dean of Harvard Law School; he repeatedly argued she has a “wealth of experience” and is “supremely qualified.”

Yet that’s unlikely to win over many Republicans.

Since her nomination was announced in May, GOP Senators have outlined a host of issues they will question Kagan on, including her decision to limit military recruiters’ access to Harvard Law School while she was dean there and her work on campaign finance reform and abortion during her time in the Clinton administration.

Even Republicans who have been fairly quiet on her nomination acknowledged they will use the hearings to pepper her with questions on her positions.

“We’ll probe her thought processes, challenge some of her statements … try to find out for myself and the country who she is in terms of judicial philosophy,” said Graham, who also serves on Judiciary.

“She comes from a liberal activist background. That’s OK as long as it doesn’t bleed over into the arena over which I believe she would take that liberal activist background and use the robe to carry out that agenda,” Graham added.