Both are considered formal correspondence, essentially literal, as literal as possible, or whatever buzz word predominates in the field today.
Both are based on the Critical Text (NT = UBS4/NA27).
Both are produced by conservative, evangelical translators.
Frankly, the ESV has the edge on sales due to the people promoting it (John MacArthur even came out saying that it it the "most accurate" translation on the market today which is why his MacArthur Study Bible is coming out this summer in the ESV (also augmented with LOTS of more graphics and eye candy).
The HCSB has some odd idiosyncracies: Messiah for Christ, Yahweh, etc.
From a readability standpoint, the HCSB is more readable. For example, in direct discourse, they employ contractions.
If the "literal Greek" reads: "us go let us to the temple," the ESV would translate: "let us go to the temple" and the HCSB would render it: "let's go to the temple." The HCSB is just as literal, but more idiomatic English.
But, frankly, it is such a losing battle, that I don't think it is worth it to try to get people using the HCSB. There are GREAT resources keyed to the ESV (ESV Study Bible, Sproul's Reformation Study Bible, and the upcoming MacArthur Study Bible, etc.). Why adopt an idiosyncratic translation with little hope to become a "standard" (despite its name)? About the only really good resource keyed to the Holman is the Apologetics Study Bible. This would be a reason to buy it for use, not for preaching from it. But even here, the Apologetics Study Bible is helpful for what it brings to the table that is unique but not as a general study Bible.
Decades ago (before DVDs), video came out in Beta and VHS formats. Beta was superior in almost every way, except for market share. Within a few years, people with Beta machines and tapes were buying VHS format and they quit manufacturing the Beta. I view the HCSB as a Bible with a future of limited market share due to the strong reception for the ESV (cf. the CEV or any number of other translations that never really caught on in the market). If you want a critical text Bible, I would advise you to jump on the ESV bandwagon. Piper, Sproul, MacArthur, etc. are a formidable block of influencers.