Zeus gives you a little more control, by allowing you to create channels and connect to any LSP - This allows you to setup the amount of liquidity you want within that channel. It's online 24/7 (there's an option to fully run in the background, or "catch-up" when it opens. Payments are always received, just the LNAddress payments need to be redeemed by opening the app).

Phoenix to my knowledge connects solely to ACINQ as an LSP.