A few things:
- Because the app uses iCloud Sync, your sync speed between Mac and iPhone is going to be throttled to 10mbps MAX. It has to go up to the cloud, then back down from the cloud. No matter which way it goes (Mac to iPhone, iPhone to Mac, it will hit that nasty asymmetrical 10mbps limit.
- The old app synced over USB, which would be MUCH faster. Even USB 2 can achieve 480mbit/sec. Almost 50 times faster than your 10mbps throttle.
- The maker of that app missed an opportunity and a market by not providing some way to sync locally over WiFi. Typical local WiFi should be able to give you at least 100-500mbps. Your download speed is poor, we'll deal with that in a minute/
- Do you see how silly it is to send data up to the cloud and back down again to get the data a few feet between your phone and your Mac?
- Let's at least fix your "30-35 download" problem, though that isn't going to fix the sync problem, because that's already at least 3 times the speed you need, since you have the 10mbps limit. Please download this free speed test app:
https://itunes.apple.com/us/app/cloudcheck/id722428563?mt=8
It has a speed test similar to SpeedTest, and the stupid thing will make you use it once. So, go ahead and do that first. But the really cool feature I want you to try is called Wi-Fi SweetSpots(r). (Yes, that's a registered trademark...) It will let you walk around your house, and show you your Wi-Fi performance between your phone and your Wi-Fi router or access point. You can turn off the annoying "geiger counter" sounds if you want!
This will tell you if you have a local WiFi problem, while not confusing this with Internet speed.
- Somebody else earlier suggested you make sure you are using 5gHz to connect to the router. I poo-pooed it at the time, because you hadn't mentioned the low 30-40mbps download speed. Make sure you have given DIFFERENT NAMES to your 2.4gHz and 5gHz beacons on your router (sorry, I don't know how to do that on your router, but surely somebody here will know how), so that you can easily select one or the other on your phone.
- 5gHz will give you the best performance if you are near the router. The signal doesn't go through walls well, so you will have less interference from neighbors.
- 2.4gHz may give better performance if you are several rooms away, for the same reason. It goes through walls better. But you WILL also face more outside interference.
Wi-Fi Sweetspots will help you sort out the local WiFi performance.
- BTW, WiFi sweetspots may saturate your router, and your router might briefly think it is not connected to the Internet. (That is what happens to me when I test with it at 5gHz). The sweetspots test is just a local test between your phone and router, so don't freak out if Netflix dies while you are doing the test!
- If you have a big house, you might need to go to a mesh router setup. A friend has had good luck with the Google hotspots, though some of the tech blogs are not so hot on it. Ubiquiti is the gold standard (used in hotels) but NOT cheap!
- I get 960mbps with WiFi Sweetspots in my office (where the router is) and anywhere from 60-600mbps in other parts of my ~1000 sq ft condo on 5gHz with what is now a pretty old ASUS RT-AC88U. On 2.4 gHz I get 185mbps in the office, and from 75-150 in the rest of the condo. This is consistent with what I would expect: 5gHz will give you higher speeds if you are close to the router. 2.4gHz will give you greater range and more consistent results, at the detriment of raw maximum speed.
- FWIW, I have a 1gbps symmetrical Internet connection through WebPass (now owned by Google Fibre). Real world performance - I consistently get in the range of 800mbps up/down with my Mac Mini or iMac Pro running SpeedTest, and 400-600mbps on an iPad going through the router. I pay $0 a month for this. (OK, the HOA pays $30/month, so in reality I guess that's what it's costing me...) AND I cut the cord and got an over the air recorder, so my total TV bill is Netflix and Hulu. Yes, you can all drool now.
- One last thing. (This IS an Apple forum...) If you have 4G in your area, you would certainly best the performance syncing FROM the phone TO the Mac by going off WiFi on the phone, and just using the phone carrier network for the uplink. Of course, it won't help performance the other way. (FROM the Mac TO the phone.) Depends on where you are. I'm on the edge of a busy downtown, and the performance isn't that great. At a previous residence, though, I consistently got 50mbps on ATT 4G. (And get this away from home.)
- Your iPhone 6 is probably fast enough.
- Final takeaway: because sync has to go up to the cloud, and back down, you are limited to 10mbps. Your router is NOT the problem, but you can probably improve your local WiFi performance, if that matters to you. (For other things). If you just don't like the way the router looks, get a new one.

(But it will probably be an ugly, geeky looking router out of a science fiction movie like mine...)
I now give it a toss-up it's either:
- the app is slow internally when you have a lot of cards
- it senselessly sends and re-sends data it doesn't have to, perhaps due to the smallest change (such at the last date you looked at the card)
- it is limited by your 10mbps upload speed
- some combination of the above