OK, so this is a pretty big topic, and I'm mostly going to speak about the US.

The United States was pretty much accepted as the best power to find yourself in the custody of, with the UK very closely on its tail. Of the slightly over 1,000,000 prisoners captured during the war ^1 by Anglo-American forces, the mortality rate was under one percent, compared to 4 percent for British and American prisoners in German custody and 25 to 33 percent when in Japanese custody. And of course the Germans and Soviets were even higher, with German prisoners of the Soviets at 36 percent, and the reverse at 58 percent.^2

Both the British and Americans were quite fortunate in being able to place their POW camps far away from the fighting. British camps in the UK or various overseas possessions posed little threat of escape, and American run camps located in the United States were even more isolated with escape attempts almost unheard of. Combined with the comparative lack of food shortages that plagued Germany and the Soviets, this factor played a large role in the treatment prisoners there received, as noted by Wallace:

With greater space and resources, the comforts of prison life in these camps were in many ways superior to those for even regular civilians in Europe. Many German prisoners would even come to describe their time in captivity in the United States as “wonderful years” and “the experience of their lives.” ^3

There also, of course, was the spectre of reciprocity, as captors knew that tales of abuse reaching the other side might result in retaliatory behavior towards their own imprisoned soldiery. German, British, and American treatment of each other was generally good, with the Americans especially being considered sticklers for following the Geneva Convention, and Archibald Lerch, in charge of the POW camps in the US certainly believed this played a part:

The War Department has an abundance of evidence which leads it to believe that our treatment of German prisoners of war has had a direct effect in securing better treatment of American prisoners in Germany.^4

The International Red Cross usually had access to the camps and helped to keep an eye on things and report on treatment from an objective standpoint. In theory care packages could be sent through the Red Cross, but as I understand, the US was almost exclusively the power to make use of this, sending its captured servicemen 28 million packaged during the war, while packages in the other direction were much rarer, especially coming out of Germany.^5

Even without care packages though, Axis POWs in an American run camp had it pretty well, all things considered. The laws of war allowed the use of enlisted men in labor as long as it was not too dangerous and not directly part of the war effort, such as manufacture of munitions. This meant that many were involved in agriculture or similar labor intensive endeavors such as logging, mining, and so on^6. ~50,000 Italian prisoners alone provided "ten million worker-days of labor" through 1944, which needless to say perhaps, freed up Americans for other jobs in war industry or the military.^7 In total, the POW population of Axis prisoners reached 425,871 in May, 1945.^8

Prisoners doing this work were paid a small wage, but it wasn't voluntary (Officers could not be forced to work however), so refusal met with repercussions. But assuming you did work, and got your pay, you could spend it in the camp store for small treats like sweets or beer, and in many cases spend it outside the camp (Prisoners were paid in scrip, not actual money, but exchange could be made for things like this). Prisoners would place orders with local companies, such as Camp Mexia where prisoners took a liking to fresh flowers, ordering 50 dollars a day from the local florist^9!

The camps themselves had varied amount of amenities. Many of them were originally army bases, so relatively decent. Prisoners were well fed, compared not only to camps in other countries, but compared even to American troops in the field, as they were provided with the same 'chow' that any other stateside Army canteen would provide, considerably better than the C-Rations in the field. Many would have theaters where they would put on prisoner produced shows, and the prisoners would create schools to provide further education to their fellow soldiers (Fully accredited by the Reich Ministry of Education!), and correspondence courses at American Universities were also offered. Sports leagues were created, often with local townspeople coming to watch a POW soccer match to pass the afternoon.^10 Prisoners were often trusted to leave the camp unguarded, and Krammer relates an amusing anecdote in this regard:

At Camp Foley, Alabama, a group of POWs remember when they were entrusted to return a farmer's automobile and were stopped by the Alabama police for speeding along a country road. "I still remember the expressions on those two highway patrolmen when they finally caught up with us," chuckles Alfred Klein. "They started to write out speeding tickets when they realized we were POWs. They were absolutely speechless! I still laugh about it today."^11

Officers, as noted, did not have to work so could pursue more leisure activities. They were allowed separate quarters, and could keep an enlisted aid. Within the camp, they still could enjoy privilege of rank and would expect the enlisted troops to treat them accordingly.

As noted, escape attempts were rare, but a few happened. In many cases, the prisoners more went through the motions without expecting to succeed. The few able to make it out stood no chance of leaving the US, most having no understanding of even the local geography, let alone the vast expanse of the US as a whole. A sheriff in Illinois, remembering a few escape attempts, stated:

[T]hey made us feel kind of sorry for them, these German escapees. We would find them there, in the streets, without a word of English, in Bloomington, in Peoria, in Galesburg; or else in the woods, completely lost like strayed sheep. Yes, I tell you, it was rather pitiful. Besides, local people weren't afraid of them. When they met up with one, they called us; we came, put a hand on their shoulder, and gently brought them back to camp.^12

In the case of the very few "successes", such as Reinhold Pabel, they never made it to Germany, but rather were ble to blend into American society. Pabel settled down in Chicago, only to eventually be caught in 1953 and deported.^13

After the war, many prisoners not only remembered their captivity with fondness, but even desired to return to the US. Surveys of prisoners during repatriation reported that 3/4 "left with an appreciation and a friendly attitude toward their captors"^14 and while the US maintained no records of it, estimates suggest that at least 5,000 former German prisoners emigrated to the US following their release.^15

So anyways, that is the sum of it. Sure, they were prisoners, but the lot of a POW in American custody, living one of the hundreds of camps spread around the country, wasn't that bad. Regimented and confined certainly, but many prisoners were accepting of their lot and did their best to enjoy their time, and the attitude expressed in this letter home from 1943 was quite common:

There is room for approximately 2000 men here. The wooden barracks are all equipped with electric lights and individual cots with quilts. The wash-room and showers may be used at any hour. The food is excellent and plentiful. Particular attention is given to the state of our health. . . . After everything we went through it is just like a rest-cure to be here.^16

Hope that helps a bit! Happy to provide follow up best that I can.

^^1 ^This ^excludes ^those ^captured ^after ^the ^war ^ended, ^which ^were ^not ^considered ^prisoners ^of ^war ^due ^to ^controversially ^labeling ^them ^'disarmed ^enemy ^forces'. ^You ^can ^find ^more ^info ^on ^them ^here, ^with ^this ^old ^answer ^I ^wrote.

^^2 ^Life ^and ^Death ^in ^Captivity: ^The ^Abuse ^of ^Prisoners ^During ^War ^by ^Geoffrey ^Wallace, ^Loc. ^273

^^3 ^Ibid ^Loc. ^274

^^4 ^Ibid ^Loc. ^279

^^5 ^The ^Neutrals, ^by ^Denis ^J. ^Fodor, ^p.191-193

^^6 ^See ^History ^of ^the ^Prisoner ^of ^War ^Utilization ^by ^the ^United ^States ^Army ^1776-1945, ^by ^George ^G. ^Lewis ^and ^John ^Mewha, ^p. ^126-140 ^for ^more ^in-depth ^look ^at ^the ^various ^jobs.

^^7 ^Wallace, ^Loc. ^325 ^It ^should ^be ^noted ^that, ^ironically, ^the ^Italians ^were ^technically ^Allies ^by ^then, ^having ^capitulated ^and ^changed ^sides ^in ^1943, ^but ^the ^importance ^of ^POW ^labor ^meant ^that ^there ^was ^reluctance ^to ^free ^them, ^simplified ^by ^unrealistic ^requirements ^on ^the ^part ^of ^the ^Italians ^to ^effect ^repatriation.

^^8 ^Nazi ^Prisoners ^of ^War ^in ^America, ^by ^Arnold ^Krammer, ^p.271-272

^^9 ^Ibid, ^p.64

^^10 ^Ibid, ^p.51

^^11 ^Ibid. ^p.74

^^12 ^Ibid. ^p.133-134

^^13 ^Ibid. ^p.71

^^14 ^Ibid. ^p.263

^^15 ^Ibid. ^p.266

^^16 ^Ibid. ^p.75

Just to clarify, are you asking about camps run by those nations, or ones where POWs from those countries were being kept?