I'm also an S7 user and have both an EE and Three contract. EE for my phone and I use a 3 SIM in a MiFi for home internet/broadband. The unlimited data on Three is unmatched here in the UK, I use 100GB+ most months with no issue, measly 2GB on EE which is constantly overrun. Would drop my EE contract as I don't find the benefits worth it over Three where am I located but I wont pay myself out of contract, and it would be a lot less than yours (half). I Got a BTS pretty close to home at street level so get 60Mb/s down / 30Mb/s up on the three SIM.
You'll never get the higher speeds on Three as you can on EE. They don't support any carrier aggregation so you'll be using a single carrier always, usually LTE1800 and rarely LTE800. On EE default is LTE1800 with lots of sites having LTE2600 too and rarely LTE800. London has the fastest configs with Wembley at the top being 3 carriers (2xL2600 &1xL1800), so fast with the right device. The demand and sites for the higher speeds is in the higher density areas so it does average out a fair bit, unless your sat in Wembley on your todd. It's also ridiculous being able to use your month's data allowance in a few mins...
You could use all your 20GB allowance in under 7 minutes sat there
For 3G (probably no one interested these days), it's pretty much equal as most cell sites share the equipment so you'll find very little between them.
Three is more than reliable these days despite the old sigma the network has. In fact I see more faults on EE than Three personally. Coverage wise EE is better, will depend on your area as to whether it's something that'll affect you. In fact a lot of the differences will come down to your location. If you're E1 postcode you'll find EE much faster in that area.
Sorry, bit of a ramble, hopefully something useful to someone in there
Work in the industry so give us a shout if any questions.
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