Pegged sidechain vs. Lightning Network? How is the Elements Project's pegged sidechains concept similar to and different from the Lightning Network's payment channels concept?
Although Lightning Network is completely different and maybe not best to compare both, things that are easier with Elements or only possible with Elements right now:

Issue assets: https://elementsproject.org/elements-code-tutorial/issuing-assets

Confidential Transactions (Amounts hidden)

Hardware Wallet for Liquid(An implementation of Elements)

Tether (USDt)

TDEX: Protocol to build decentralized exchange for trading assets issued on Liquid (An implementation of Elements)

Simplicity: https://github.com/ElementsProject/simplicity

Covenants: https://medium.com/blockstream/cat-and-schnorr-tricks-i-faf1b59bd298 (Maybe soon possible on Bitcoin as well)


LN is also possible on an implementation of Elements: https://twitter.com/notgrubles/status/1355547472827834373
Few differences between Lightning Network and Liquid (An implementation of elements) mentioned in https://blog.liquid.net/six-differences-between-liquid-and-lightning/

Transaction size: the size of payment each Lightning channel can process is limited by the size of the initial funding transaction used to set it up. This makes it less likely that, as transaction size increases, a complete pathway from buyer to seller will be found, making the Lightning Network less reliable for large transactions.
There are no limits to the size of a transaction on the Liquid Network (technically 21 million BTC would be the limit!). A user can peg in as much BTC as needed and start transacting immediately. Recipients also do not need to engage in any channel preparation, they can receive as much as a sender can send. Since Liquid operates on its own blockchain, the number of transactions it can handle is subject to a blocksize limit Fees are currently very cheap (0.1 sats/vbyte for next-block confirmation), but as Liquid adoption grows fees are expected to increase which will make micro transactions unviable on-chain.

Speed: Payments via the Lightning Network can be made almost instantly. Since Lightning payments do not require confirmation on the blockchain they can take place as quickly as an internet connection will allow: potentially allowing for millions of transactions per second.
New Liquid blocks are produced at regular one-minute intervals—ten times faster than the average Bitcoin block—and two confirmations are required for a transaction to be considered settled. This means that Liquid transactions take around two minutes.

Privacy: a degree of monitoring is still possible with Lightning since individual nodes can record the channel and direction information from transactions they are asked to process. While this method of surveillance has limitations, it still represents a privacy concern.
In contrast, the Liquid Network’s protocol is designed so that the amount of funds and type of asset transferred are not revealed to anyone other than the sender and recipient. This is made possible by a cutting-edge cryptographic protocol developed by Blockstream called Confidential Transactions.

Trust model: Liquid’s trust model is based on a federation consisting of 15 hardware security modules (HSMs) attached to host servers (known as functionaries). The functioning of the BTC:L-BTC two-way peg relies on two thirds or more of the Federation functionaries acting honestly.


LN privacy issues are also explained in https://abytesjourney.com/lightning-privacy/