Is weight or size a concern? -> LiFePO4.
Lifespan? Much higher with LFP. Lead acid approx 500 cycles at 50% SOC.
Capacity: 200Ah GEL = approx 100Ah usable maximum (with decreased lifespan). LFP: approx 80Ah usable capacity
Plenty of time to charge: Doesn't matter which you choose
Limited time: LFP can charge more, since the charging current is higher, whereas with lead the charging rate highly decreases if the battery gets at a higher SOC. (LPF only drops at the end)
Environment: LFP can't be charged at <0 celcius. At 5 celcius, they can be charged, but not recommended to do high charge rates. Leadacid can handle freezing temperatures better.
So yes, it all depends on the application. In general I prefer LFP, but there are some cases where it's better to use lead.
Note: A 2000W inverter can't generally be run at full power with a fet-based BMS, they generally max-out at 120-150A. For higher currents you need a contactor based BMS, or rewire the inverter to run directly from the cells (bypassing the BMS), and only using the BMS to remote control the inverter so it still shutdown upon cell issues