European MSc vs MEng in CS when applying for PhD in the US?

I've read other questions regarding MEng vs MSc when applying for PhD in the US. However, those questions were from people studying at US universities, and I have a question about transition from European Master's to US PhD. From what I've seen Master's programs in Europe are quite different from those in the US.

I am finishing my Bachelor's studies, and I am applying for several Master's degree programs (Machine Learning/CS) at different universities in Europe with plans of applying for a PhD in the US after that (my financial situation and the fact that my Bachelor's is a 3 year program, prevent me from applying directly to a US graduate program). One of the the programs I applied to is MEng. I've read that research experience is crucial when applying for PhD, but unlike MEng at most US universities, this one has a Master's Thesis (but no other research). Then again, MSc programs I applied to also lack research except for the Master's Thesis.

My questions:

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  Is there a difference between European MEng with Thesis and MSc when applying for PhD in the US?

  
  


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  What can I do to improve my chances of getting accepted for a PhD if I choose MEng?