I'm not 100% sure but I don't think this is strictly accurate. I was researching this topic and came up with some findings.

Let's take one of your examples where ETH is going up against USD but BTC is going down against USD.

Let's say 1 ETH=100 USD today. 1 BTC=1000 USD. The ETHBTC value would be very very close to 100/1000=0.1 (you can verify this with any trading pair).

Now let's say ETH goes to 200 USD and BTC goes down to 500. The ETHBTC value would again be very close to 200/500=0.4
This matches up exactly to what you said. There's a 4x gain with ETHBTC compared to only a 2x gain with ETHUSD. All good, but the story doesn't end there. Eventually our profitability would always be judged by USD values (until the day we won't need to cash out any more).

So the story goes on.

Let's say I purchase 1000 USD worth of BTC when BTCUSD was 1000. That would give me 1 BTC. I use this BTC to buy ETH which is trading at 0.1 (100 USD) and end up with 1/0.1=10 ETH.

In time, the ETHBTC value goes up to 0.4 (situation explained earlier). I decide to sell them and get 0.4*10=4 BTC. That's awesome, I started with 1 BTC, now I have 4.

But is it really?

BTC has fallen to 500 (from 1000 originally). My 4 BTC is now worth 2000 USD.

What would have happened if I decided to save my exchange fees and trade with fiat?

I invested 1000 USD when ETHUSD was trading at 100. That gives me 10ETH. I sell when ETHUSD is 200. That gives me 2000 USD.

Surprise, surprise...this is exactly the same as with the USD ->BTC->ETH->BTC->USD transaction. I gained nothing. Probably lost a few percentage points trading BTCETH on exchange fees.

Hope this helps. Please feel free to punch holes in my theory.