In general, Any sports for the matter, Non-vegetarians have a better advantage than the vegetarians.

Quality of protein:

We all know that protein is a combination of 20 amino acids. 8 are called essential amino acids (EAA) which means the body can not manufacture them and has to be supplied from the outside via food. The other 12 are non- essential amino acids, means that the body can produce on their own.
Most of the vegetarian sources of protein other than milk are deficient in or or more EAA. Yes even the so much spoken about soy is deficient in one EAA.
When it comes to animal sources, not only they are rich in EAA, but in some forms like the RED MEAT, the radio of aminoacids are exactly the same as that of the human muscles. That makes it very much useful for sports people.

Recovery:

We spoke enough about amino acids. When it comes to post workout recovery, constant supply of EAA round the clock ensures very quick recovery and possibly supercompensation of nutrients in the muscles.
When the recovery is optimal then the strength gains are going to be optimal too.

Conclusion:

When considering the odds from nature, when an individual follows a well periodized plan for strength gain. He/She gains more strength with a balanced meal plan with plenty of non-vegetarian in it compared to only vegetarian meal plan.
There have been some extremely strong vegetarians in this world, but that’s exceptional cases.