There are many things to consider when coming up with a contract that's fair for all parties involved. Sometimes an artist wants to gain experience working on a big project with a well-established client, so they agree to a contract that gives away most, if not all, of their rights. Sometimes a client is trying to start a new business or cares a lot about their company's intellectual property, so they pay an artist an extra fee in order to lock down the copyrights to a work of art that's important to them. The type of contract an artist and client might use depends a lot on what they're each looking for and what kind of project they're working on — so it's good to get clear about what both parties expect as soon as possible.
A type of contract that will hand over all the rights to an artwork to the client is called a "work for hire" contract. It's useful when the client is a big publisher whose business relies on its intellectual property being thoroughly protected. An animation studio like Disney, a video game studio like Valve, or a card game publisher like Wizards of the Coast are good examples of companies who hire freelance artists, but set up contracts that let freelancers retain very few rights to their own work.
For an artist, the main downside of a "work for hire" contract is that the client can expect to derive all of the future value from the artwork, while the artist can expect to derive almost no future value from it (besides some exposure). This means that if an artist exclusively works on projects under a "work for hire" contract, they have to keep finding new clients and new projects in order to make more money. Artists can't use any of their previous work, in original or modified form, in future projects — and they can't license any of the work they've already done, now or in the future, to other clients.
"Work for hire" contracts only become more of a burden for more talented and experienced artists, who are forced to watch from the sidelines while the value of their hard work is maximized by savvy clients who know how to turn a simple character or illustration into a core part of their brand or business. Entire media empires have been formed on the backs of hardworking artists, working for little pay, under "work for hire" contracts. Many artists only realize they've severely undervalued their work several years — or even decades — after they've finished working on it and sold away all of their rights to it.
For clients, the main downside of a "work for hire" contract is that they will probably end up paying a much higher fee for an artist's services under this type of contract — especially if the artist is an experienced professional working at a design agency or is someone who cares a lot about creating a well-known brand for themselves. Also, clients may find that some artists are a little less invested in producing artwork that they'll immediately lose their rights to after it's paid for. It's hard for any client to replicate the feeling that an artist gets when working on a character or story that truly belongs to them, even if they compensate the artist well.
There are many reasons an experienced artist will charge more per hour for a project that's under a "work for hire" contract, but it mostly comes down to the fact that professional artists know how valuable their work is. They're no longer trying to build out a portfolio of work or feeling guilty about charging money for doing work that they enjoy so thoroughly — they're singularly focused on creating their own business that's sustainable, and they know that being denied the rights to their work removes a massive amount of future value from their portfolio. If a freelance artist wants to prosper in the creative market, one of the first things they discover is how much it costs, in terms of money and time, to run a real business.