Does DNA being circular or linear directly affect the speed of DNA replication?
I am not sure if I well understand what you mean by directly affected.
I will list some possibilities below (For reference you can see any genetics textbook, I use, Genetics: A conceptual approach by Pierce, but I guess any textbook would do).

Porkaryotic polymerases (usually processing circular DNA) have a higher nucleotdie per second speed than eukaryotic polymerases (processing linear DNA). Does this mean that shape directly affects speed? In this case I would say no. It's just a difference between prokaryotic and eukariotic polymerases. Some prokaryotes have linear chromosomes and their polymerase will still be faster than eukaryotic polymerases.

One prokaryotic chromosome has only one origin of replication, while one eukaryotic chromosome has several of them, so that eukaryotes parallelize even in a single chromosome. Does this mean that shape directly affects speed? In this case, I would say yes. Due to steric effects, the shape of the chromosome has to do with the ability of having several origins of replications, even if the lengths are the same. Edit: After Ved's comment, I realized that this is also not necessarily true. Not all circular chromosomes have one single origin of replication; archaea have circular chromosomes with more than one origin of replication

Linear chromosomes are easier to unwind. Does this mean that shape directly affects speed? I would say, yes for large chromosome and no for small chromosomes. Edit: After David's comment, I realized that I am not really sure that linear chromosomes are easier to unwind. A Wikipedia entry states this, but I gave a look at the paper they referenced and found no real statement about this.


Importantly, if the DNA molecules you compare are one prokaryotic and one eukaryotic and they are very short, I would bet my 5 bucks on prokaryotic (circular) being faster, because in absence of all the parallelization the eukaryotic DNA polymerases are slower than prokaryotic ones.