does the mRNA more closely resemble the DNA strand from which it was transcribed?

Although mRNA copies one of the DNA strands precisely, after it is processed, it will have some differences compared to the DNA template strand.

Messenger RNA copies one of the strands of the DNA double helix which is called the template strand. The base-pairing rules apply-In DNA, adenine pairs with thymine and cytosine pairs with guanine. If the DNA template reads TAC GGC, the messenger RNA would read- AUG CCG. The reason there is a U in the second position of the first codon is because RNA lacks the base thymine (T) and the base uracil (U) is substituted. The DNA is copied into mRNA which is facilitated by the enzyme RNA polymerase along with transcription factors which are proteins. RNA polymerase assembles the transcript by separating the DNA at a specific point and joining RNA nucleotides that correspond to those in the DNA template strand. RNA polymerase joins DNA at the promoter region. 

Once a stop codon is reached (UAA, UAG, UGA) --the process of transcription stops. The mRNA transcript is called pre-mRNA because it must be further processed into mature mRNA. This entails splicing out sections of RNA known as introns which are stretches of DNA that don't code for a protein and splicing together exons-protein- coding genes that are needed to carry out translation and ultimately protein synthesis.

Next, a cap added to the 5 prime end of the mRNA which contains guanine, and a poly-A tail is added to the 3 prime end which consists of many adenine nucleotides. These facilitate the molecule of mRNA to exit the nucleus, travel to the cytosol and to attach to a ribosome at the 5 prime end. Also, the tail protects the mRNA from degradation by enzymes.  

The splicing and addition of a cap and a tail change the mRNA slightly from the DNA template.