Come on guys... let's stop our tribal squabbling and answer the actual question that was asked... ;-)
Generally speaking does it take more time to do it in Illustrator than on Photoshop?
It can do, in a way that isn't true going the other way. Any professional will use whatever tools are best for the task in hand. But...
- If you demand a vector image, you're saying that, if the designer's process for this task involves raster graphics (for example, if this design involves photographs, raster effects, or any of the many tactile effects that are easy in raster and tough in vector), there must be a stage of either vectorising a raster graphic, or creating in vector a graphic of a type that would be easier in raster. This is occasionally trivial and easy, but more often it's skill intensive and time consuming to do well. How time consuming is rarely possible to predict at the start.
- If you demand a raster image, you're saying that, if the designer's process for this task involves vector graphics, there must be a rasterisation stage. This is usually straightforward. If it's an effect that is better done in vector, they'll do it in vector then rasterize it. This rarely involves anything more complex than smoothing over and touching up elements that the software's automatic rasterization borked up slightly.
Do I have to account for more time if I require it to be done on Illustrator?
Any time you put down a restriction or requirement on the tools any professional can use, that will limit their flexibility and on average will increase the time it takes.
Will forcing Illustrator ever speed a task up? No, because if Illustrator is the most suitable tool for the task, and you put no restrictions on what tools can be used, they'll use Illustrator anyway, because it's the most suitable tool for the task.
Will forcing Illustrator slow a task down? It might, it might not. Because it might slow things down, and won't speed things up, in your estimates you need to factor in some additional time - not because of anything about Illustrator, but because you're placing a restriction in order to get a specific end result.
It would be the same for any professional. If you hired a plumber and told them they could only use hammers, they'd charge more even if the task looked like it only needed hammers, to factor in the risk of encountering something unexpected where a hammer wasn't the best tool.
(the implied question) Will demanding vector graphics cost more?
Generally speaking, yes.
As you know, vector graphics have certain advantages over raster graphics which means - all other things being equal - they are often more valuable to a client, and almost never less valuable (because rasterization is usually easy). In economic terms:
- More versatile end result = higher demand
- Possibility that the process will require an additional skill-intensive stage = job that needs a higher time estimate + possibility of an extra mandatory skill type being required = scarcer supply
- Higher demand + scarcer supply = higher price
There are always exceptions. Some people might always design in vector so they wouldn't charge more: but their prices may be higher on average. Sometimes, some straightforward tasks can be predicted to be done purely in vector: but you'll need a really really clear brief and some negotiation. Some designers are desperate for cash but remember the golden rule of design pricing.
In general, on average, briefs with "Must be vector" in the specification list will have higher prices on average than briefs that don't.
(the question nobody asked) Which is better, raster or vector?
Which is better, screwdrivers or hammers? It depends on the needs of the task.
(the question people don't ask enough) Is UI design work always about using Illustrator (or inkscape, coreldraw...) and/or Photoshop (or gimp, photopaint...)?
No, consider Fireworks. It's an underrated option that in many ways offers the best of both vector and raster, and has features like master pages that are particularly suited to UI and web design.