One of the considerations you have to make, when thinking about such things as decreased battery, is whether it actually matters that you're getting higher speeds. Remember the 'speed' you're taking about is the bandwidth, how wide the pipe is. You're likely getting better ping times from your wi-fi than over cellular. In the end, does it really matter if you're opening a webpage on a 20Mbps stream or a 5 Mbps stream? It's still going to feel the same unless its laden with huge graphics that take forever to load. It's likely that the ping times would slow you down on LTE vs wifi but it's probably not even going to be that noticeable.
If you're listening to Pandora or iTunes Match songs, it's just downloading in the background. It really doesn't matter if it took 20 seconds or 40 seconds because it's loading in the background while playing. You're not going to catch up and buffer. Both connections are fast enough to make the experience seamless.
I don't know how your wifi Internet connection is. Mine is rock solid reliable and has been for over 10 years. I've never had fluctuations in speed. I can't say the same thing about LTE at all. I frequently get a rollercoaster of slowdowns and speedups. One speed test may say I'm at 18Mbps and a minute later it says 2.5. I've never had consistency in LTE in any way.
As DeaconGraves said above me, you're also taking your phone off your network. I use my phone and iPad with my AppleTV frequently.
