That's a good question, but unfortunately we can't discuss it here without being accused of "shilling." 
Because you don't have an answer more likely. Monero has yet to solve this. Another thing Monero has yet to implement is tree pruning, which will be very important for dealing with blockchain size
BTW for anybody who doesn't know, I feel the need to point this out. Monero was created for the sole purpose of implementing Cryptonote. So when somebody says "monero like" ring signatures what they're really talking about is implementing Cryptonote. Monero has nothing to do with it.
Monero has everything to do with it. Your ignorance is showing.
There are very good reasons why Vitalik wrote "monero-like" instead of 'cryptonote-like.' You just don't know those reasons.
Here, I'll help. Pay attention!
Monero has fixed, improved, and built on the canonical Cryptonote implementation, which is called Bytecoin.
https://lab.getmonero.org/
Thanks for the update! I'll try it out now too. Maybe you or someone explained this already, but how does the regular update work? Does it restrict tx sizes by denying large size transactions and couple the larger ones with the higher fee? Or are all tx's going to have the same fee you set regardless of size now? What's different with the experimental update 0.8.8? Does it scale on the medium block size or something?
It's a fairly severe bug introduced by TFT. The penalty free block size is the median block size (right now ~20kb), and block reward decays exponentially with block sizes that are larger than the median block size. The maximum block size is 2 * median block size, and as you approach that you rapidly approach a reward of zero. When TFT replaced the old tx mempool getblocktemplate generating code (which had a bug that caused blockchain halting), he made it so that all tx would be included in blocks regardless of the penalty they incur. This is why we're seeing problems now with block reward.
In my update, I have limited the maximum possible penalty incurred to about 9% of the block reward (so at worst instead of 16.5 you get ~15.0 MRO, and aren't penalized any more than this). The median block size will now grow more slowly.
The ideal behaviour, as proposed in the cryptonote paper, is to only include tx with fees large enough to compensate for the penalty. I'm not sure this would even work as they intend as the incentives are kind of bizarre (it probably incentivizes hoarding tx and not sending them to other miners so you can reap larger rewards). I will be working on a more elaborate fees and penalty algorithm for the mempool, but this will have to do for now.
The severity of the issue may be directly observed here: http://monerochain.info/charts/reward
State of Monero: 2014
May:
- fixed the block reward penalty mechanism and dynamic block sizing
May:
- fixed the block reward penalty mechanism and dynamic block sizing
None of this answers any of my questions. Monero has not found a reliable way to reduce the blockchain size, period. You have alluded to some of the tricks they put in place to moderate it, but nothing they've implemented is a solution. At its core Monero is a cryptonote implementation with a few little quirks to solve some minor issues, nothing more.
Back to my original question though, how does anonymity benefit Ethereum?
The CryptoNote blockchain bloat problem has already been solved. Monero takes a cautious development approach but at some point I expect they will implement a solution close to the one explained below (which already works):
http://boolberry.org/files/Boolberry_Reduces_Blockchain_Bloat.pdf
Pruning is more than possible. It has already been done by Boolberry! Ethereum can also implement pruning if it wishes.
