"Better" is subjective and I'll try to be as helpful as possible.
Which one is better depends on what you value. There are many different things that users value, but here are some of the most common:
Will the computer do what you need it to do?
How long before performance starts to suffer?
More money usually equals more power
Does the computer have the ports you need to connect your external devices like hard drives, monitors, etc...
So, here are some more detailed examples of the above.
Simply put, will the computer be able to run the applications that you need it run? Some applications require much more power than others. For the common everyday apps (Word, Mail, Calendar, Chrome, Firefox, Safari, etc...) either the MacBook Pro or MacBook Air at its minimum will handle these tasks with flying colors. Only when you start looking at specialized apps like Photoshop, After Effects, Logic Pro, Final Cut (filmmaking, photography, audio production), will you need to consider a more powerful computer. The MacBook Pro generally offers more power depending on configuration of processor, RAM, and graphics card.
As time goes on, new applications and websites will require more power. Therefore, your minimally-powered computer from 2010 will have trouble doing simple things like opening an email. If you buy the most powerful computer available today, the odds are it will continue to be powerful enough for lots of years to come (about 5+ years). If you buy a minimally-powered computer today, it may only be a few years before performance starts to suffer (about 3-5 years)
Most people need to consider price as a limiting factor. You'll need to find a happy-medium between performance and longevity - that is - the most powerful computer your budget can handle that will last you as long as possible.
The MacBook Pro often comes with more or different ports for connecting different or multiple devices at a time. Your external monitor may need a type of connector that one computer doesn't offer. Best to verify that you will be able to plug in your devices.
There are other things to consider including screen resolution, graphics performance, I/O specs, but I'm speaking to the most general concepts for the average person. We could spend days scrutinizing all the little differences between the MBA and the MBP.
My opinion is that for most everyday tasks, a MacBook Air and MacBook Pro are effectively the same. Buy whichever one suits your budget. I would go with the MacBook Air for everyday tasks as it's far less expensive and will perform just fine for several years.
If you need a powerful workhorse that can handle heavy workloads for years to come, a customized MacBook Pro will be the better choice.
Hope that helps!