To first order, the differences stem from one's view of the efficacy of the sacraments. Now, as a reformed Baptist, I fall squarely in the TR camp (which is also viewed as the low-brow camp by the CRs). Now even within the TR camp, there are different views on the degree to which something supernatural occurs at the Lord's Supper or at baptism. But it is reasonable to say, I think, that Baptismal regeneration is a taboo for the majority of TRs and acceptable (though not the in same sense as the RC view) to many (most?) CRs.
The interesting battleground for this debate doesn’t even really involve reformed Baptists (I have never met a CR Baptist, such a person is difficult to imagine), but the Presbyterians, who may be the frozen-chosen, but can certainly thaw quickly when it comes to this topic.
The rallying points for the debate tend to be the details of sola fide (does grace administered through the sacraments dilute justification by faith alone?), the necessity of baptism (most claim it is necessary, but some say it is "more necessary" than others), whether children should be given communion (are we excommunicating our children?), etc.
As a TR, I think the CRs tend to quote Calvin selectively (no doubt they would launch the same criticism in my general direction). And that they quote theologians and councils, relative to scripture, at a higher ratio than the TRs (I'm willing to dig my heels in and duke-it-out on that point). But I am biased. I also think that the sections in the Westminster Confession on the sacraments are the weakest in terms of their proof texts (no doubt that’s the Baptist within). I also think, proof-text issue aside, that they do not teach what the CRs sometimes claim—but hey, that’s for the Presbyterians to sort out.
What brought me to this subject is a little nugget of a comment from a related post on Mark Horne’s blog. The comment was (in answer to an expressed despair over our present-day diluted view of baptism, and an inquiry into the origin of this deplorable state of affairs):
the influence of contemporary evangelicalism and the worry that we look too much like Rome. it's a crying shame.What this comment is saying, I think, is that modern Evangelicals (and TRs) mindlessly apply a single litmus test: If it smells like Roman Catholicism, it’s bad. It’s an ad hominem attack and, as such, is useless, even if true, (which it isn’t) since it offers no support for its claim. It is just a lament that the opposition is dumb and has no regard for truth of an assertion; no it is only important to ask how "Roman" it is. Such arguments, since they contain no content, are easily invertible (into something equally pointless), such as saying the CRs reflexively reject anything that doesn’t bring us into better alignment with Catholicism.