Is Airport Express reasonably better at receiving Wi-Fi signals than a laptop? I keep my router (an Apple Time Capsule 2011) in my living room, but I frequently use my MacBook Pro Retina 15" Mid-2014 in my kitchen, which is separated from the living room by a wall.

In the kitchen, I get roughly 50 % of the download speed that I get in the living room near the router.

I'm thinking of getting an Airport Express to extend my network via Wi-Fi extension. If I were to place it in the kitchen, would it suffer as much receiving penalty as my laptop, or is its capability much stronger, thus warranting the placement to some degree?

Alternatively, I could place the Airport Express in the hallway connecting the living room with the kitchen, effectively "mid-way" between the two rooms.
You could assume the Airport Express uses practically the same chipset as pre-AC equipped Macbooks.  Knowing this, any Airport Express would perform less fast than your 2014 laptop which does have AC.

But... Your 2011 Time Capsule also doesn't have AC technology, so this wouldn't be an issue.

Placing the Airport Express in the kitchen will theoretically improve signal because the Airport Express doesn't have (doesn't need) battery power saving routines as the Macbooks have (need).  Therefore chances are higher it can establish a better connection to your Time Capsule.

The bad thing is that you cannot improve speed with this; degraded signal in the chain is irreversible, no matter what (weakest link remember).

The good thing is that your Macbook wifi radio won't need to suck as much power as it will connect to a much closer antenna.

But... if you can place it in the middle the signal will have less chances to degrade and you benefit in speed AND battery.

So, yes, your footer assumption is the way to go; place it in the hallway.

If speeds are really really important to you and you have a little more money to burn, upgrade your network with a new Time Capsule or a new Airport Extreme.  These baby's do run on AC technology which is day and night different in speed.  Or invest in a non-Apple AC capable router.