Yes, a wired connection would be better than a potentially spotty Wifi signal. Running ethernet (Cat 5e or better) will provide you with the best results.
However that isn't your only option, and certainly not the easiest.
First which version of Time Capsule do you have? And I'm assuming you are using the Express as a repeater?
Unless you live in a mansion (and/or massively spread out) and you have the newest version of Time Capsule (2013 lol) I would just try to centralize your modem and router than do away with any repeaters. The WiFi AC versions of the Time Capsule and AirPort Extreme do a great job with beam forming. Naturally wireless AC does have as good of range as wireless N however with the wireless AC spec beam forming is incorporated into the spec and can generally have a longer range. Plus if you are dealing with something that can buffer the extra bandwidth can come in handy (aka 50% of 100 is better than 75% of 10....purely an example). This is a good place to start because you can experiment with it, see if it works, and if it does investigate locations.
For example my parents have a very large rancher. The Comcast guy connected a modem/router combo in the basement where the cable comes in. Half of the house had terrible signal. I bought them an AirPort Express and it was moderately better but what I ended up doing was pulling a Cat 5E up and into their kitchen island and putting the router in there (there was electric I was able to splice into for a junction box). This easily covers the entire house now. While there are better routers I've never had one that was so reliable (perfect for parents).
You can also extend your network via power lines (electrical wiring in your home). I have zero experience with them but I've heard decent things. To dumb it down (since I don't know specifics) you plug an adapter in the wall by your router and hook ethernet too it, plug the accompanying adapter in by your ATV and hook and ethernet to that. And that is it. While there is overhead you should still have enough bandwidth for the ATV. And they probably make wireless models and stuff.
Like mentioned a repeater reduces overall network speed because its using up more bandwidth by retransmitting the same data which is the reason I try to avoid them.