The choice between Bitcoin and Monero on a Tor market is not a philosophy debate. It is a tradeoff between how easy the coin is to get and how much of your transaction it shows. Here is the tradeoff in numbers, so you can pick based on your situation rather than your opinion about coins.
Confirmation times
Bitcoin credits a market deposit after two to three confirmations. Each confirmation is a block, and blocks arrive roughly every ten minutes, so a Bitcoin deposit takes ten to sixty minutes to credit, depending on how busy the network is. Monero credits after about ten blocks, and its blocks are shorter, so a Monero deposit takes roughly twenty minutes, with much less variation. If you need the balance fast, Monero is the more predictable one. If you are not in a hurry, the difference does not matter much.
Fee exposure
Bitcoin fees are set by the network and they spike. On a quiet day a deposit costs cents. On a busy day the same transaction can cost several dollars, and the fee is paid by whoever broadcasts the transaction, which for a deposit is you. Monero fees are flat and low by design, a fraction of a dollar regardless of network conditions, because the protocol prices them differently. If you are making small, frequent deposits, the Bitcoin fee variance adds up in a way the Monero fee does not. For a single large deposit, the difference is negligible either way.
What the chain shows
This is the part that actually matters for privacy. Bitcoin's ledger is public. Every address, every transaction, every amount is visible to anyone who looks. A deposit to a market address is a public event, and if that address is ever linked to you, the transaction is too. Monero hides all three of those things. The amount, the sender and the receiver are concealed by ring signatures and stealth addresses, so a deposit on Monero leaves a far smaller trail on a readable chain. The honest framing is that Bitcoin gives you convenience and Monero gives you privacy, and the right choice depends on which of those you value more for this particular purchase. Neither choice changes your escrow terms. Both get identical protection under the multisig contract.