Scope recommendation for SCA

[zzattack]

Apologies for probably yet another one of 100 similar topics, although I have a somewhat specific use case in mind.

I'm looking to do some side channel analysis where two specific scope properties are highly beneficial:
 - high frequency since we must typically oversample an unknown asynchronous clock
 - excellent facilities to get the traces onto desktop PC for post-processing; up to 1M traces is not uncommon

Two candidate series are under my consideration and I'm looking for some advice on which way to go.
1) is a USB3 picoscope which excells in the PC interfacing but budget limitation would not stretch beyond the 200MHz 5444D or 300MHz,  perhaps the 500MHz 6424E if I really _really_ stretch it
2) a higher-end Chinese like the 800MHz Rigol DHO4804, allowing for an affordable 800MHz

I do not believe 12-bit resolution is a necessity since it comes at cost of sampling frequency, but this is mostly unfounded.
Features like picoscope's rapid block acquisition seem very very useful for SCA. On the other hand, with 'only' 200/300MHz within budget, we hit limitation in the range of devices where we can apply 10x oversampling.

Can anyone recommend one over the other for my intended purpose?

[alm]

Another option if you want to consider used it to buy an older Windows-based scope that allows you to do processing directly on the scope. I know for example that Lecroy WavePro 7000(A) series and WaveRunner 6000 series and their later scopes allow you to write software in a number of programming languages that can directly interact with the acquisition system and sample memory. See XDEV Advanced Customization Package. The advantage is likely lower latency / higher throughput and more bandwidth for your buck. You might be able to find a 3 GHz WavePro 7300A for $1000-2000 plus shipping from the US. Downside is generally no warranty, the front panels are flimsy and will likely have cracks in them, and you'll be developing for Windows XP or maybe Windows 7 for more modern scopes in that range, like the WavePro 7 series. For at least the WavePro 7000 series there are solutions for getting the XDEV option.

I don't know if other Windows-based scopes like Tek and Agilent/Keysight offer similar features. I'm guessing not since they do a lot more processing in ASICs instead of on the main CPU.

New scopes that do the same will likely require you to take out a second mortgage on your house.