What are the pros and cons between these LED under cabinet lighting options?
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.