You will do similar types of projects as a consultant at a firm, but will have to make do without a team or any of the resources you normally have.
Going independent is great if you want more flexibility while also getting paid more. If you're taking a career break, are starting a family or just want to increase your rates it could be a fit for you.
If you like the support a firm offers you - the resources, engagement managers, stable salary and team culture you might struggle as an independent.You will also have to spend some of your time doing sales to find projects, and won't be able to see your work through to implementation most of the time.
The biggest benefit of working for a firm is you don't have to worry about finding work. Going independent means part of your job now includes sales. Try using platforms like Expert360 and searching job boards with "part-time" and "contract" filters turned on.
Working for yourself means no bonus, no equity, and you even have to pay your own super.
Whilst you won't be able to climb any particular corporate ladder, exposure to lots of companies and problems will open doors for you.
You won't be learning any new skills you can take elsewhere, but the consulting toolkit you will continue to hone is always useful in organisations.
Shifting projects every 3-6 months will help you build relationships with teams across many companies. Depending on the type of work you're doing, you might even work with a lot of the organisation.
You can choose when you work and what projects you take. It's common for independents to do 4 day weeks, or to take long breaks between projects.