I imagine that combat-experienced soldiers would have been an advantage on a new front, but I can see how this might be outweighed by the costs of transport as well as the differences in terrain. I'd be interested to hear any info you may want to share. Thanks!
EDIT - I suppose I shouldn't limit the question to just the U.S., so I welcome stories from other countries as well
Here are three examples. Alexander Patch was sent to New Caledonia with a regiment of draftees to combine them with a disparate collection of other preexisting Army formations on Samoa and New Caledonia to form the 23rd US Army Infantry Division, which is also known as the Americal Division. He led that division in the middle phase of the long battle of Guadacanal. Patch was promoted to command the XIV Corps, which consisted of the Americal and 25th US Army divisions, plus the Second Marine division. The XIV Corps won the battle of Guadacanal. In late 1943, the US Army sent Patch to North Africa. There he took command of the Seventh US Army and used this formation to execute Operation Anvil-Dragoon, the invasion of Southern France. Patch commanded the Seventh Army until the fall of Germany, in May 1945.
Joe Lawton Collins was the commander of the 25th US Army division at the battles of Guadacanal and New Georgia. In 1944, he was sent to England to take command of the VII Corps of the US First Army. Collins thought the planners of operation Overlord were woefully underestimating the amount of artillery ammunition they would expend and wanted more. His concerns were dismissed and he was told that his experience in the Pacific theater was "bush league". Collins retorted that the Japanese Army bush league compared to the German Army and that the US Army was going to need a lot more ammunition than was being planned.
Going the other way, Curtis Lemay was the commander of the 305th US Army Air Corps bomber Group that flew deep penetration missions over Germany in 1943 and early 1944. Lemay was sent to China to take over the XX US Army Air Force and then sent to Tinnian to take over the XXI Air Force and oversee the strategic bombing attacks of Japan.
At the lower ranks, one example is Carol Wood Espy jr. He was a Navy combat medic who was at Omaha beach on D-Day. then Espy was sent to California for nearly six months of rest and relaxation in southern California, before being sent to Iwo Jima in February of 1945.
Source for Carol Espy was the WQED television special about World War II veterans, aired in 2009.
My paternal grandfather served on an LST as a sailor. His boat was supposed to be at both the D-Day and Okinawa landings, but thankfully for my dad and I they were late for both. I don't know if he counts since he was not a soldier, but he did serve in both theaters and saw combat.
My grandfather was a coast guard medic attached to the attack transport ship USS Bayfield and went ashore in the invasions of Normandy and, later, Iwo Jima. He said Iwo Jima was much worse.
Funny thing is that he signed up for the coast guard thinking he would just be part of submarine patrols on the US coast...and instead ended up in the two bloodiest battles of the war.