Have any armies equipped/fed their officers and enlisted men equally?

In theory, there were no ranks in the People's Liberation Army in 1965

As a result of the Cultural Revolution, ranks were abolished in May 1965.

Technically I suppose that doesn't fit your question - since there were no officers, Officers weren't fed equally. I am also skeptical that the innovation worked very well.

I agree with @spyder in that I think equality never happened for both historic (officers' roles descended from noble men's) and practical (clear separation helps discipline at least in certain situations) reasons.

Perhaps communist countries subscribed to nominal equality in their lower ranks to some degree. However, here is one anecdotal evidence from Jung Chang's Wild Swans: Three Daughter of China for actual privileges awarded to officials (and presumably also officers) that speaks to facts on the ground. Since her book on Mao I consider her a biased source, but this account has always staid fresh in my memory, because her mother was pregnant at the time and she eventually lost the child due to the hardship on this long march:

After they had crossed the mountain there were several deep, fast-flowing rivers in their path. The water level rose to her waist and she found it almost impossible to keep her footing. In the middle of one river she stumbled and felt she was about to be swept away when a man leaned over and caught hold of her. She almost broke down and wept, particularity since at this very moment she spotted a friend of hers whose husband was carrying her across the river. Although the husband was a senior official, he had waived his privilege in order to walk with his wife.

My father was not carrying my mother. He was being driven along in a jeep, with a bodyguard. His rank entitled him to transportation -- either a jeep or a horse, whichever was available. My mother had often hoped that he would give her a lift, or at least carry her bedroll in his jeep, but he never offered. The evening after she almost drowned in the river, she decided to have it out with him. She had had a terrible day. What was more, she was vomiting all the time. Could he not let her travel in his jeep occasionally? He said he could not, because it would be taken as favoritism since my mother was not entitled to the car. He felt he had to fight against the age-old Chinese tradition of nepotism. Furthermore, my mother was supposed to experience hardship. When she mentioned that her friend was being carried by her husband, my father replied that that was completely different: the friend was a veteran Communist: In the 1930s she had commanded a guerrilla unit jointly with Kim Il Sung, who later became president of North Korea, fighting the Japanese under appalling conditions in the northeast. Among the long list of suffering in her revolutionary career was the loss of her first husband, who had been executed on orders from Stalin. My mother could not compare herself to this women, my father said. She has only a young student.

Beside the lofty aim of fighting age-old nepotism, as cited by a still proud daughter, this (Western) reader also gets the sense that there was peer pressure and the need to avoid offenses from possible rivals driving the father's stern decisions: just as one might expect as usual, unfortunately ...

I know that in the British armed forces there has always been a difference in equipment/clothing/food/messes between officers and enlisted men/women.

For example, the British Army at it's earliest was constructed of militia etc. commanded by the local nobility/land owners - which was an extension of the feudal system. As things have modernised and developed the system was edited and eventually became a meritocracy. For example in the Napoleonic War era a Regiments officers had often purchased their commissions and payed their way up the rank structure - a practice that started in 1683 and didn't stop until 1871 - the officers were richer, and often payed for personally tailored uniforms and weapons.

The difference in armament/clothing between non-commissioned and commissioned ranks began to reduce after the industrial revolution but still persists today to a limited extent due to the different job roles required of different ranks, and in ceremonial activities, for tradition - an example being the difference in dress uniform for officers of the RN and the Ratings, or that on parade officers still carry a sword where as non-commissioned ranks carry a rifle (the exception being mounted regiments).

In the UK we still have a mess system that includes a Officers Mess (or Wardroom in the RN), Chief Petty Officers/Warrant Officers/Sergeants Mess for Senior NCOs and a Junior Rates/Junior NCOs mess for Junior NCOs. Obviously, in the field commissioned and non-commissioned ranks eat the same rations.

The French Légion étrangère has the closest interaction between officers and soldiers that I know of. For example, they all spend Christmas or any other official holidays together. Officers are as well expected to be able to do what the soldiers do and frequently have to. My experience of Legionary officers and homme du rang is that they share more in common than not. Note that 10% of officers come from the ranks.

Note that if we had a légionnaire here, he would be able to expend this answer...