A strong WiFi signal sips charge. If the WiFi radio can turn down the power and maintain its connection, it'll have little to no impact on your battery..... conversely, a bad Wifi link will devour your battery. And while the same still holds true with LTE, it'll still use up a charge quicker than a good WiFi link, no matter how strong it is.
But a good T-M LTE link is like a direct pipe into the internet backbone..... dat speed!. I never get a really good LTE link at my house, but if I did, I would consider dropping off my home WiFi and sticking to LTE... damn the battery hit.