What you're asking is a pretty broad question. It really depends on what hardware is used in either the laptop or desktop chosen, as those parts will determine how much power is going to be used.
If you are looking at costs for lifespan or malfunctions, desktop computers are generally a lot easier to repair and maintain, as you have the option of replacing any part needed. If you have an issue with a laptop, typically you can only replace the hard drive or RAM, and in very rare cases the GPU may be replaceable. But that only assumes only those parts are the issue. Usually if a laptop goes bad or you want to upgrade, you need to purchase a whole new one, as opposed to upgrading a single part in a desktop. Costs for repairing a desktop vary as well, depending on your personal knowledge and how much the part (if there is a hardware issue) costs. If you have an issue with a laptop, you will likely have to have it sent out for repairs.
If you aren't concerned about mobility, I would personally recommend a desktop computer, as it will last you a lot longer and will be easier and cheaper to upgrade in the future.
I agree with Genericuser. In terms of reliability and longevity, not to mention repair options, your best bet would be a desktop. Now, if you prefer mobility, it may be worth the risk of buying a laptop. Remember, heat is the ultimate killer of electronics and due to the lack of room in a laptop, there is more heat produced, which has the potential to shorten their lifespans, regardless of the manufacturer.
If you go with a desktop, you could easily build a decent machine yourself at a cheaper cost than ordering from someone like Dell, etc...