To directly answer your question: currently, ethereum has the same fundamental scaling problems that bitcoin has (limited global throughput)
Bitcoin's attempted solution on this front is off-chain scaling via lightning network. As far as I can ascertain, this has had highly limited adoption.
Eth's attempted solution on this front is sharding. I can't claim to be an expert in this, but from my understanding after proof-of-stake is deployed, ethereum plans to deploy something like 64 separate "shards" which, from my understanding, are like extra blockchains for conducting transactions, and using some kind of complicated proof of stake system to keep it consistent. In this case, while the main-net still has limited global throughput, scaling up to add more side chains will allow scaling additional throughput. You can read more here https://ethereum.org/en/eth2/
As with lightning, we don't know how well this will actually end up going until it's deployed.
Ethereum has set aside sharding temporarily to focus on PoS. The plan to scale in the short-term is to use technology called "rollups" which put a transaction's signature data off-chain while keeping its data on-chain, effectively "batching" a bunch of transactions into one.
Eth has a sidechain called Polygon with orders of magnitude more usage than bitcoin's lightning network. There are a number of other promising "scaling solutions" launching in the coming weeks. Sharding is unlikely to happen in 2021.
Bitcoin's attempted solution on this front is off-chain scaling via lightning network. As far as I can ascertain, this has had highly limited adoption.
Eth's attempted solution on this front is sharding. I can't claim to be an expert in this, but from my understanding after proof-of-stake is deployed, ethereum plans to deploy something like 64 separate "shards" which, from my understanding, are like extra blockchains for conducting transactions, and using some kind of complicated proof of stake system to keep it consistent. In this case, while the main-net still has limited global throughput, scaling up to add more side chains will allow scaling additional throughput. You can read more here https://ethereum.org/en/eth2/
As with lightning, we don't know how well this will actually end up going until it's deployed.