I'm ready for a bit of flaming on this one but IME rugby is 'safer' in the private sector (3DC, mixture of state & private education). DS3 is, to use a pp's words, a 'rugby school' and the Rugby coaches are very separate to the PE teachers. They also start playing tag and touch in prep school or the junior part of the school if it is an integrated one like DS's where they go right from 4/5 through to leaving for Uni so by the time they start playing contact rugby they've all already got c.6 years of rugby skills training.
Likewise, they have superb equipment (way more than DS1's 2 state schools) and more of it for practising scrums and tackles.
HOWEVER.... To kinda prove it's still not that safe even in the best/most trained of environments - DS3 (HUGELY experienced player for a 14 year old AND one of the 5'10'' jobbies to boot) was tackled badly really fucking dangerously in a match last year, lifted off his feet into the air and fell backwards with the head hitting the ground first - on to a January grass pitch which was, to all intents and purposes, concrete given the conditions. He felt fine so didn't say a word to anyone
and match officials didn't see that he'd fallen backwards (if they had he'd have been removed from play immediately) tho they HAD seen the illegal tackle and player was booked.
Was only a few hours later at home when he was acting a bit odd & I started to grill him about his day and the match in particular when he said 'yeah, wll I did bang my head a bit after this guy lifted me 2 foot up and I fell back..' 
Spent the evening being ob'd in A&E as had clear case of concussion...
I was fucking LIVID that they'd seen the tackle but failed to clock the nature of the fall and thus allowed to play on - as THAT is when it really is super dangerous, one concussion and playing on and then incurring a second whack to the head can, literally, be lethal. He wasn't allowed to return to contact sports for 4 weeks.
As a side note, the school revised their policy in light of his concussion and all players are now required to report any fall they see to a match official even if the player in question insists they are 'fine'.