Yes there are ways to make Bitcoin transactions slightly more private but they're not inherently private like Monero's are.
Also XMR doesn't suffer from inflation, just tail emissions.
Discussion
Tail emission is a massive bug, this means there is no cap and there is no way to know how much is in circulation. The proof is in the footing
Tail emission isn't a bug it's intentional for mining security. Bitcoin is taking a risk that tx fees alone will be adequate and consistent enough to pay miners once block subsidy runs out. Tail emission is less inflation than gold which has been a money for thousands of years. You can run a node or add up block rewards (they're transparent when first mined) to know how much Monero is circulating.