I would say you get quicker by doing quick runs (necessarily short) and gain endurance by doing long (and gradually longer) runs, so why not both.
I've always done fine on 2 runs a week - one short (10k) pushing the speed all the way and one long (15-20k) trying to maintain the pace I set out on (which gets faster as you get fitter). No serious injuries in 30 years of running because no overtraining. And I guess my performance has been OK - best half M (on hills) in 1:30. And the approach scales up - I did the London M in 3:30 on one short run (15k) and one long run starting at half M and getting longer up to almost the whole distance, every week, over about 6 months.
If you're in this for life, then the only thing I can add is - new shoes every year, and run off-road as much as you can. That way hopefully your knees won't quit on you in middle age.
I'd say that there's a difference between tired legs - when you have just run 10 miles and are still going, and stiff legs - when you ran 10 yesterday. A whole set of different things are happening in the muscles then. Also the next day you've replenished your glycogen levels in muscles and liver. Doing a longer run gets you used to dealing with muscle cramps and running out of energy. They say a marathon runner hits the wall around 20 miles (I know I did the one time I ran one), but when I was doing my first couple of halfs something very similar happened at 10 or 11 miles - aches and shakes. So either the training since then has allowed me to store a lot more energy, or I started running more efficiently, or probably both.
Jimo - that might not be as hard as you imagine... the course is gloriously downhill for most of the last two miles - if you're in ok shape at 11 miles it'll probably be the fastest half-mara finish you'll ever do.
Hmm. Well the last time I did that run ... let me see, when was that ... oh yes, yesterday, there was a 30metre climb in the 12th mile - which can be hard work if you're a bit tired by then. The 12 mile marker is just after the top of the hill.
Or there's a whole different approach, which I don't see advocated in these forums much - I run twice a week, or once if something in real life gets in the way. Usually 4/5 miles mid-week, 10-13 Sunday. I must be a real slouch, right? Not really - I always push my speed, trying to do the best time I can. (Slow running wrecks your posture which puts a strain on the joints, so I'd rather do an LFR than an LSR.) I'm aiming at a 1:45 half at Berkhamsted which isn't too bad for a 49yo. 10 years ago I did a marathon in 3:30 with the same plan (but longer runs of course). I hardly get any injuries because I'm never over-tired, I always want to run and I have plenty of time for everything else. And I expect my knees and hips to still be working when I retire.