Different across the pond
Living in your most-loved ally across the pond, I can say things are generally different here. Our police will show up for (just about) any reason that you call them, and generally relatively quickly. Granted, if it's a busy time and they're receiving too many calls for service, they will prioritize and it may be quite some time before you'd see them about a call for, say, graffiti on your building. But an active burglary, with the perpetrators still on-site, gets treated as a fairly high priority in most jurisdictions around here (though, as I'm sure is the case everywhere, calls from upscale, low-crime neighborhoods may get answered faster than those from poverty-stricken, high crime ones, but that may simply be due to those jurisdictions being better-funded).
While every jurisdiction is different (and we have a crazy mix of state police, county sheriff departments, city police and sometimes specialty forces like university campus police here), from all of the articles I've read from Vulture Central over the last few years, it sounds like ours generally do a better job of showing up and investigating. Whether you'll enjoy the experience may be a different story, as the reports of questionable police activity seem to be higher here (just read a story this morning about a poor fellow who got tased 11 times, including directly in the twig and berries). Personally I've always been treated.. well, I can't necessarily say "professionally", but at least "as reasonably as I feel you can expect from the police" in my few encounters with them, but then as I'm a reasonably affluent white guy I don't think most people would trust my my experience to be representative..