Blind Pick: Own team synergy is the only concept to worry about. Enemy team is unknown, so you can basically just play what you want and experiment strictly with your own team comp.
Draft Pick: Enemy team comp matters now too. Banning out key members that hold a team comp together (Think Malphite for a Yasuo Comp) that would counter your team. The real advantage is just that you can bring runes that have more significance and change your summoner spells. Overall, draft encourages team play A LOT MORE.
---> EX: I know my lane match-up is a counter to me, so I'll instead run Exhaust/Teleport to alleviate a "safe" laning phase. Or, since I'm against a (Burst mage) I'll have flat health yellows instead of armor. Knowing who your opponent is in setup and being countered is still better than not knowing, and then fighting a Vlad with practically useless 9 armor for 12 minutes.
I honestly don't get why people even play blind pick if they want to just call lanes anyways to be honest. I thought the entire point of blind pick was to play a specific champion and not get it banned in champ select.
TL;DR: The point of draft is you can prepare to be countered in a specific way, and show your ability to play as a team, rather than display individual skill.