Let me start off by saying I'm not really an advocate either way. Both have their plusses and minuses in my book.
The AIOs are EXTREMELY easy to install once you have your basic wiring figured out, and they do everything you'll need in a single box. You don't have to worry about additional parts because it's all been put into one package for you. No more extra expenses, which is really nice and appealing. The downside is, if something breaks or goes wrong, your entire system is down.
With individual components, you have to buy every little piece. You would need the inverter PLUS when you get solar panels, you would have to invest in a solar charge controller (or possibly several) to provide the ability to recharge from solar. On the plus side, if your charge controller goes down, you can still use every other aspect of the system till you replace it (and it doesn't matter what SCC you replace it with).
The standalone units don't have to worry about cramming multiple components with multiple functions inside. They only have to perform a single task (invert/charge/etc). The All In Ones (AIO) have to get all these different components happily working together in a single package and sometimes compromises are made in the quality (which is why sometimes things break).