My view on the subject is that "it depends" on where the learning curve requirement came from. Here's a couple scenarios to consider:
- The client hires you on the basis of doing one type of work, and then throws a new technology that they require you to use. Because the requirement came from them, you need to make it clear that you are charging for the learning curve.
- Your company is standardizing on certain technology stacks to make it easier to move developers across projects. Because the client didn't ask for the technology, but your company did, they pay the cost of training--i.e. the learning curve.
- You stumble on a cool new piece of technology that looks like it can really help. Neither your client nor your company asked for it, so you'll have to spend your own time learning it. Once you've got a good working understanding and it's clear that it will solve problems at work, you can set up a technology introduction session. Some companies reward this type of activity. If the company/client agrees to use it, then they pay as the rest of your team gets up to speed.
There are quite a bit more scenarios that can play out here. For example, if a project is stymied by the current algorithm/design, and the client needs a certain performance or feature you can't currently get, then the client will most likely pay while you work out the alternatives.
The important issues are: is this billable work, is this addressing a process problem, or is this for my own curiosity? If it is billable work, the client pays. If it is a process problem, your company pays. If it is curiosity, you pay. The toughest choice is when the line isn't really that clear between billable work and employer concerns. If you see that you can gain a competitive edge by learning a new bit of technology, then the lines start to blur between your own personal responsibility and your company. Propose it to the company saying you want to spend some time researching it. The worst that can happen is that they tell you to do it on your own time.
Finally, if you are expecting the client to pay for the learning curve, make it clear to them that is what is happening up front. They will either back off of the new whiz-bang technology they asked for, or they will agree.