How is my bounty cost determined?
The minimum amount of Gold required to place another Chieftain on the bounty list is determined by how big their Empire is and the number of times they have been bountied in the past 24-hrs. Having a bigger Empire makes you a much higher profile target. You can view your base bounty cost from your profile in the "User" tab.
The person may have purchased property differently or faster than you. They may also get more money from their inner circle allowing them to buy more property. They could have purchased cash using FP (Favor Points), use FP to purchase other items and extra clan. Then there is the option of purchasing FP for more of these items.
They may also be online the majority of the day/night playing if they have the available time allowing them to do more missions, earn extra cash, catch bounties & level.
In answer to your second question, a player with 300 chieftains can easily win against a player with 1050. They may have all their skill points into attack & they use weapons that are high in attack. When you attack back & all you see are random weapons you may be only seeing the weapons chosen for defense not attack. If they are winning you may want to look at your defense points & what weapons you're using to defend. There are so many different variables. It's not cut & dry, thats what makes it so fun!