Both striking and grappling can be very effective in a street fight. But, when attacked, you should always look to get out of a fight as soon as possible. Striking ends fights a lot quicker, so in terms of self-defense, striking has a slight advantage over grappling.
Is it better to start with grappling or striking?
If you're training martial arts for self-defense, it's best to start training a grappling art like wrestling or Jiu-Jitsu. Striking depends on fleeting moments of success to stop a threat, grappling is the art of controlling a threat.
Are grapplers better than strikers?
Grappling arts have proven to be more effective in MMA fighting than striking. In the early days and before cross training, MMA fighters were experts in just a single fighting style. We saw many style vs. style matchups in which grapplers were dominating strikers.