The photo quality will be similar but the a6000 will have higher megapixels (24mp vs 20mp) and higher ISO sensitivity (25600 vs 12800) for low light scenes. The zoom on the DSC-RX10 will be 24-200mm (35MM FORMAT EQUIVALENT). The advantage for choosing RX10 over a6000 will be built-in image stabilization and weather sealing for shooting under extreme conditions.
You will find this help guide link below useful for setting up your a6000 to connect to your iPhone.
Connecting this product to smartphone
Send to Smartphone Guide