Hello,
I want to ask what is better Solo mining in my own built node and Private pool or Public solo mining pool something like solopool.org , how much effect public pools have on my solo mining efforts to mine any coin specially if there's a competition in the same pool , other pool with higher hashrate on the same pool ?
The total hashrate of the pool doesn't count, because only YOUR own shares can actually find you a block and pay you for it. The hashrate of others doesn't count, there is no "competition".
The more hashrate you own yourself, means the more shares you send, so the more likely you are to find a block. That's the only thing that counts: what others do on their side will never concern you in solo mining.
To answer your question, it's best to use an honest solo pool that has been paying its users for a long time:
-solo ckpool
-viabtc
-kano
This doesn't really change anything compared to building your own pool, but at least with one of this 3 solo pool you'll be sure that from a technical point of view everything's ok, and you won't risk investing energy, time and hope, for nothing.