I have seen this issue reported several times on this forum with no apparent solution yet. An iPhone hogs all the bandwidth when it connects to Wi-Fi. This could be explained if the router has QoS enabled and it gives the iPhone a very high priority but this is unlikely in your case. You could try giving Apple feedback here http://www.apple.com/feedback/iphone.html or perhaps call AppleCare and report it. It could be a bug.
Regardless below is a User Tip I wrote about Wi-Fi issues just in case one helps.
1) Perform a Forced Restart: Hold down the Home and Wake/Sleep buttons at the same time for about 15-20 seconds until the Apple logo appears. Allow device to restart.
2) Reset Network Settings: Settings > General > Reset > Reset Network Settings. Rejoin the Network again.
3) Reboot Router/Modem: Unplug from power for 2 minutes and plug again. Update Router Firmware (check manufacturer’s support website for a newer FW). Also try different bands (2.4 GHz and 5 GHz) and different bandwidths (20 MHz recommended for the 2.4 band).
4) Change to Google's DNS: Settings > Wi-Fi > Click on the Network, Delete all numbers under DNS and enter 8.8.8.8 or alternatively 8.8.4.4
5) Disable device prioritization on the router if this feature is available.
6) Determine if other Wi-Fi devices on network are working well (other iOS devices, Macs, PCs).
7) Try device at another Network, i.e., neighbors’, public coffee house, etc.
8) Restore the Device (ask for additional for details if desired).
https://support.apple.com/en-us/HT201252
9) Go to an Apple Store for hardware evaluation.
User Tip: https://discussions.apple.com/docs/DOC-9892
