I've been trying to find a secure and private wallet solution on bitcoin chain but it's quite a challenge. There seems to be downsides with every solution. I started wondering if things might be better on ethereum chain if I would keep wrapped btc there. I know that must be triggering to read this on bitcoin forum but please be open minded when you continue reading and then we can objectively discuss this.

That's why this topic is about the comparison on privacy between Ethereum and bitcoin. I don't necessarily mean eth vs btc coins. I mean the blockchains and everything we currently have built on them, not in the future or the past.

Both blockchains have by default bad privacy because they have completely open and transparant ledger. But it's still possible to have some privacy although how much is up for debate.

In bitcoin you have to do coin control to not mix UTXOs. You absolutely need your own bitcoin node otherwise coin control doesn't matter. You need TOR to hide your IP. VPN is unreliable and easier to trace than tor. For example, they can see which VPN provider you use. Another example if if you conjoin and almost everyone else us using TOR, and the few who use VPN all use a different provider. That means you are maybe the only one who used the vpn provider and then when you take the btc out on the other side you use the same vpn provider, easily tracked. Lastly you need coinjoin.

In ethereum I am not sure I understand everything. But instead of not mixing UTXO you should do same thing but not mix accounts aka addresses. Ethereum node requires a huge investment so we can't expect everyone to run their own node. What privacy penalties does that have? Maybe not having a node in ethereum isn't as important for privacy as it is in bitcoin? That would be convenient if that is the case because it takes a lot of resources to to run a bitcoin server (an SSD with 2 TB storage capacity). Additionally it seems that even if you had your own node, you can't run it with TOR (http://whonix.org/wiki/Ethereum#ETH_vs_Tor_generally). There are many "mixing" smart contracts and networks on ethereum so at least there ethereum has the advantage over bitcoin.

Lets evaluate which has better privacy. Or maybe they have almost the same level of privacy?
As a bonus, if it turns out many of us think that ethereum has equal or better privacy, we could also discuss the security between having btc on bitcoin vs having wrapped btc on ethereum.