Maintaining the integrity of the structure of your content is the biggest migration challenge.
As mentioned in other posts, as you grow more comfortable with the technology behind your website, you will inevitably reach a point where the direction you want to take your operation outpaces or loses alignment with the purpose and utility of the platform that has served you up to this point.
The primary challenge you face is that the internet indexing mechanisms that let everyone know where all your content was has expectations about your material where your pages are, where your images are, and so on. Typically these structures have given you solid ranking, and if you have had your site in place for a long time, the last thing you want to do is suddenly disrupt the traffic flow you have built up on your current platform.
In the past there have been a number of approaches that could be taken to mitigate downtime and search engine confusion. The best way to smoothly transition from one structure to another is to build parallel structures and use what are called permanent redirects to convert search index result addresses from the old structure to the new one.
Some platforms provide plugins or other module features that allow you to custom map inbound addresses to redirect but if you have a very large site this could be very time consuming. An alternative that is available is to provide server-level redirects, but this method requires some technical skill to do safely, and getting the process wrong can significantly delay proper indexing of your new site.
For WordPress we typically use the Redirection plugin which has been supported for over a decade and provides a relatively straightforward management interface that allows for uploading batch remappings of content addresses.
ProcessWire provides its own internal redirection mechanism the Page Path History core module that automatically indexes and redirects requests from prior addresses to wherever they sit in the current structure. This provides an elegant straightforward path for updating from an outside platform to processwire. The initial content can be batch migrated as it existed in the initial site structure, and then the developer or editor can reorganize that same page content into a new structure and all of the old content addresses will resolve and eventually get corrected in the search engine content index.
Both WordPress and ProcessWire support XML sitemap exports for search engine content mapping, but there is usually better ranking preservation when the original results record has its address updated via permanent redirect.
For many starter web services, the simplicity of getting content in matches the difficulty of getting it out.
The secondary challenge you face when trying to move your content to a new platform is the complexity of migrating all of the content you have created, uploaded and organized from one particular structure to another. There are technical options that are available, but generally require some consultation to pull together.
At a very basic level, if the system you are subscribed to or using for free has a developer toolkit that allows for customization, there is going to be a way to extract the content you have saved to the service but it is often in a raw package state it might be a huge archive file that includes its own offline webpage navigation.
Some systems may allow for individual pieces of content to be extracted using programmed scripts. These services can be linked to the backend of either WordPress or ProcessWire the software layer acts as a bridge between the two platforms.
Some systems may provide for direct database access or if you are using a platform on your own equipment it is possible to wrap a software interface around that database and bridge database content.
Some systems provide no real back-end access at all and this is probably the most frustrating option for newcomers who feel like they were sold a bit of a bait and switch. The good news is that all web pages have predictable structures and it is possible to use scripts known as scrapers to grab your content and store it for integration into your new platform.
While all of these solutions take care of concerns regarding your original content, if you want to preserve the look and feel of what your prior platform gave you (unlikely, but possible) then that process of recreating the look and feel of your prior product may take some creative design though many of the more popular sites use popular existing frameworks or slightly modified versions that are accessible. We do our best to preserve the appearance you are used to if all you really want is more control over the content and structure of your site, we can get you there.