Many issues here. Let me go over in as much detail as possible:
Background: I love energy efficiency, and when doing my kitchen researched this LED Vs CFL vs incandescent lights extensively. Notice there are also permit (legal) implications, depending on which state you leave (CA has Title 24 for example).
Connector types: There are several connectors that make the decision of which light you can use tricky. the main ones are
Edison: The screw type, accepts CFL, Incandescent and some LED bulbs
Pins (2 or 4): Accepts florescent. Was invented mostly so that for permits purposes, they can make sure you are installing an efficient light and will not go and replace the CFL bulb with an incandescent one after you pass the permit.
GU10: mostly used for high voltage halogen
GU5.3 Bi- Pin: mostly used for low voltage halogen
High level rules:
You never go with incandescent when it is incandescent Vs CFL (Edison, screw system). LEDs are getting there, but not enough to justify the price and their light output is very low.
You can only go with pin florescent if you have a florescent "hw". that is the only thing that you can plug there by design.
Never use Halogen. If it is a GU10 (line voltage), get a $20-$30 LED (MR16). you get 4W Vs 35W. Light output is lower, but you can get HW with simply more heads. Replace 3 halogen with 5 LEDs and you are fine in terms of light and energy savings
If the halogen is a low voltage, things get tricky. You can just replace the head with a 3-5W bi-pin LED. they run $10-$20. They problem is that you need to make sure your low voltage converter will work. converters have what's called "minimal load". For most of them, they expect a 35-50W halogen so they have a minimal load of 10-20. That means that when you plug a 3W LED, they may not kick in. you solve it by either using a remote transformer that feeds "enough" LED bulbs, or get a transformer that is "led" designed, but really all it means is that it has a minimal load of 3w and goes all the way up to something (I have a 3-60W for mono-points).
Lat general tip: do not mess with dimmers. Just on/off.
My personal choices:
For kitchen recessed light I got LED LR6-GU24. It is 12W, think that the florescent way would suggest I put a 23W bulb for each of these (I have 7). That means 50% saving. Same light output (they say it is 65W equivalent, but it feels like closer to 90W). No one can tell it is LED BTW, it is bright and even (not a "pin" of light, and well spread).
Cost efficient: great! less energy, and upfront cost was the same as getting a florescent can combination. (you may get cheaper florescent if it is not for a permit and you do the Edison type)
For a bat lights I went with 3 mono points. Each has a transformer built in. I did not (suggest you never) buy "LED" lamps since you pay a huge premium for getting the LED HW. I just got the transformer with minimal load of 3W. I then threw away the GU5.3 Bi- Pin halogen and got Maxxima LED MR16. They are very good price (value) company. I compared the light to a $30 GE and these one are just as good. Notice that at 3W it is indeed just ambient light. good for over the bar in addition to some other light in the room. If you need more power, get 4 or 5W bulbs. see maxxima site
For spotlight lights in the center of medium size room, I went with much cheaper "line voltage" fixture from Lowes. These fixtures expect GU10 halogen (25-50W). I got in this case a the more expensive $30 LED GU10 bulbs (GE, at home depot). They are great, but I hope you can do better on the price. I have 5 and for medium size dining room, correctly targeted, it is nice light to use while eating.
The short answer is to check with the bulb manufacturer. Ambient temperature and use case requirements may also be mentioned on the box/packaging.
The long answer is that it depends (as always eh?). From what I could find online, CFLs and incandescent bulbs are actually MORE sensitive to LOW temperatures than LEDs. So in your specific use case, I would think you would be fine in using an LED bulb.
That being said, keep in mind that there ARE certain environments where LEDs may perform worse -- particularly in settings where the ambient temperature is very high, resulting in overheating of the LED package and eventually leading to device failure. I think most manufacturers are getting better at heat sink designs anyway so this may not be a concern later.
-M
Best Answer
The aluminum fixture is a classic fixture, comes in a box, has a power cord, you pick a spot and bolt it up and hook power to it. It also looks like some installer just slapped a couple lights under your cabinets.
LED strips are, by nature, a bespoke installation custom fit to your kitchen. It's going to look much better, though is more sensitive to the risk of an incompetent installer doing a bad job.
These strips are weird though.
First those strips are insanely overpriced; most of us pay $10 per 16 feet (5 metres). This is a lighting specialist company who is trying to be a one-stop shop for lighting contractors, and is dealing with these lights reluctantly as a sideline because they are in demand. They charge through the nose for the difficulty (for them) of supporting these "odd ducks" (to them). If anything they want to overcharge to steer their customers into their more conventional lights.
And these are 24V (the almost universal standard is 12 V). With either voltage, you are operating under the electrical code's low voltage rules, which are much easier to deal with.
The pictured tape lights are not the ones described. The pictured ones have a clear "dome" over them, which splash-proofs them and makes them easier to clean. This is one of two waterproofing options typically available, the other is a hollow silicone tube around the LED strip.
They are advising clips to fasten it, which is a good idea. Most are backed with adhesive, and this can let go after a few years.
Their strip interconnection options don't see to be very good.
They are claiming 15 watts in 60 inches which may be more light than you want. The common LED strips come in a lot of different power densities (watts per foot). This gives you great versatility, and you can alter the lighting easily after the fact as you learn what works. You are no longer married to a fixed "luminaire" that comes in a box. However, this flexibility also rewards those with real skill... an installer may need to "skill up" or get left behind.
Their recommended transformer is bulky and ungainly, there are other options. There are also dimming and multi-color options for those interested in that. Not from this company.
You can also get any color temperature you want, from 2700k incandescent-like to 4000k fluorescent-like to 5000k claw-your-eyes-out LED color.