With my iPhone 5, I had WIFI download speeds at ~1.5Mbps on 20Mbps FIOS.
My phone: "Apple" WIFI chip connecting to WPA2/TKIP
I tried:
1. Restoring as new: no difference
2. Restoring from iCloud: no difference
3. Deleted and downloaded speedtest.net app again: no difference
4. Changed my router from WPA2 AES to WEP: Went up to ~3.5 Mbps.
5. Changed my router to WPA2 TKIP/AES mixed: Went up to ~8 Mbps.
While it's not that good, it's not as painful, so I'm going to stick with #5 for a couple weeks... if people do find out that it's a hardware issue, I'm going to exchange.
At least my LTE is ranging between 20~30 Mbps, and I'm on a grandfathered unlimited plan.