Honestly? Probably neither one exactly
As someone who once had to deal with applications for a living... bear in mind your initial audience has 50 of these to read. You have no control over whether yours lands on their desk as the 3rd or the 43rd. Best assume the eyes are already glazed, fingers twitching nervously toward the long-empty cuppa. Your mission is to wake them up again, but without frightening or befuddling them. In short, keep it short. Wear your learning and your whimsy lightly: no erudite sentences that demand a double-read, and no hedgehogs unless the job is about hedgehogs.
Concretely, this means any verbiage that will probably appear word for word in most of your competitors' applications should be trimmed ruthlessly. So for example at least three quarters of the cover letters I came into contact with would lead off by stating that the applicant was "responding to your advertisement", sometimes going on to cite name of publication and date. I grew to detest this opener. We knew we'd advertised the position. We knew where we'd advertised it. And if we really wanted to know which of our ads were reaching people, we'd invite them to an interview and ask. I didn't outright discard applications which used this formula but the few which skipped it earned an immediate spark of goodwill from me, and left my brain just that little bit more wide-awake to continue on to their next paragraph.
Similarly, explain why you are interested in the position, but only in passing; pivot immediately to why the position should be interested in you . This isn't because your reasons are irrelevant, it's just because nine tenths of your fellow applicants will have more or less exactly the same reasons as you (job is well paid, in a top location, company is a vibrant startup or industry growth leader or what have you) and so the danger is that you'll all find yourselves writing more or less the same sentence here and therefore I'll be reading more or less the same sentence for the 45th time and won't be properly impressed. Unless you are confident that your own reasons for wanting the position are fairly distinctive, just pay the obligatory bland compliment and smoothly move on to yourself. What makes you special, memorable and worth an interview for this position? Again, work on the assumption your application is going to fall somewhere toward the end of a large stack and try to offer something fresh.
You don't have to re-summarize your whole professional history (that's what your CV is for) but this is the place to outline a very brief narrative arc (are you a baker turned food safety inspector turned building inspector?) that will help us remember you. It's also where you can highlight any special selling points, aspects of your CV which make you a standout candidate or which you feel are more relevant than they might seem at first glance.
Last, if you are the perfect fit for reasons that involve a little dot-connecting - say, not because it's exactly the same thing you have X years of experience doing brilliantly at previous jobs, but rather because it ties together several disparate strands of your career - say so . As boldly as possible. Don't count on us to connect the dots, we might or might not notice and you don't want your future career depending on whether or not I've had my coffee.
Yes, you probably do need to wind up by expressing that you "would be delighted to hear from us" or however you want to phrase it. But the closer that is to being the only piece of boilerplate in your entire letter, the wider awake and the thankfuller I'll be.
Yours,
the secretary with an empty tea mug and a whole stack of these things to review