Time old question - Which is better. Both have adv/disav.
On 24/7
As stated Higher electric bill, and not just from computer as it will also increase a/c (slightly). Also as stated Fans and increased dust inside case. HDD's tost-up, but probably would decrease life - But then pwr-up/dwn is also hard on HDDs.
Powering down
Two disavantages come to mind - One waiting for the thing to boot and (2) pwr-on is one of the biggest stress placed on electronics and is when most die. Primary reason is the high inrush current which can be 3 -> 5 times higher than nominal current.
Myself I alway power off at night and normally power on when I get home from work.
Wife, she normally leaves hers on - No diff in failure rate.
At work, computers are normally on 24/7 as updates are normally applied at night (Most of our our work computers are laptops). But when desktops were still common, I notice no difference in "Life span"