If you're going to continue to burn fossil fuels, it seems better to burn it in a plant that inherently captures the carbon then trying to wrangle it back after it's release. The interesting part of the Allam cycle for power generation is that supercritical co2 is the working fluid for the turbine, and when you burn the fuel it increases the mass in the closed circuit. Both the size and the efficiency of the plant also purportedly improve with the Allam cycle too.
That would be true, if the power plant has high capacity factor, and if it stationary, and if it is located near a place where the CO2 can be sequestered.
But if you (say) have peaking turbines that are intended to take over when renewables or short term storage are not available, they may have very low capacity factor. It could be economical to have them release the CO2 into the atmosphere, then steadily scrub that CO2 back out again, especially if that scrubbing could be done in a location with extremely cheap solar energy (like, say, Chile).
I'm for pursuing both options really. There are likely solution areas where both would be a win. And we really know not enough about the end direct cost of either until sufficient numbers are built out - and we should build out both to at least 10x what the prototypes do. The real problems are governmental policy, and then financial policy to get the attention and scaling going on any of these solutions.
https://en.wikipedia.org/wiki/Allam_power_cycle
https://www.netpower.com/technology/