In 2014 I travelled to the US on a non-immigrant holiday visa - I was granted a 10 year VISA, which is technically still in date but on a passport that has expired and I no longer have.

I believe that I never really needed a VISA, so I applied for an ESTA for my forthcoming trip, which I have been granted.

I was cautioned for criminal damage (under £500 - private property) in 2006.

I am now concerned that when I go through US Border Patrol and get fingerprinted, it is going to alert staff of my previous trip to the US on the VISA (technically still in date) 

If Border Patrol ask me about why I had a VISA (and now don't have one) what do I say? 

I am very anxious about the situation, but genuinely believe I can honestly say that I have not been convicted of a crime that would rule me out of an ESTA. Looking at the list of crimes of moral turpitude I don't believe this fits the bill

Your advice and thoughts are extremely welcome. Should I apply for a VISA?

Well, if you don't have the passport anymore, you can't use it, obviously. However, if you disclosed your caution for the previous visa then they already know about it, so that might be an issue, but if it is an issue, why did they give you an ESTA? It sounds like you weren't arrested for an offence that resulted in serious harm to property, so it might be that they have seen your record and are OK with you having an ESTA this time. Having said that, you have a valid visa in your name, just not in your current passport. You could always email the embassy and ask them what to do, as if you comply with what they say, they can't hold that against you. They might say you have to transfer the visa to the new passport, but it should still be easier and quicker than making a new application, as you shouldn't need an interview.

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If you are to punish a man retributively you must injure him. If you are to reform him you must improve him. And men are not improved by injuries. (George Bernard Shaw)