Network Core – Differences in Data Transmission Between Wired and Wireless Networks

Since you've clarified (comments above) that IP net/mask/gw are the same for wired/wireless clients, then your AP is bridging (as opposed to routing or NAT'ing the wireless clients.)

1. Verify the wireless systems are getting DNS servers via DHCP. If "cannot access Internet" means "web sites do not load", this may be all that is wrong.

2. Verify your Internet edge router, (and/or firewall,) isn't blocking the traffic. You might have everything configured correctly from the network and IP point of view, and then not realize that the edge router has special rules to only permit certain of your internal LAN IP addresses out. (For example, your DHCP server could be configured to give specific IPs to certain DHCP clients (the boss's desktop), while servicing the rest of the clients (eg, printers) from a pool of numbers which aren't generally permitted out to the Internet.

1) Is this guy a nutjob? Or am I crazy for wanting to stick with a cabled solution for static devices?

I would say no, not a nutjob. Nor are you crazy for wanting to keep cabling where possible. However, this is not a totally unreasonable request although it goes a bit further than it probably should. Since the network is already in place, some sort of "happy medium" would probably work here.

There are several things that are driving this type of request:

1. In the past 5-8 years, people have become much more highly mobile and like it that way. Many end users now have multiple devices they carry that are wireless from the standard smart phone and tablet to a whole slew of other gadgets (watches, light bulbs, speakers, and so on). While wireless used to be a nice convenience, today it is often a requirement to have reliable, fast wireless where ever they expect to go.
2. People hate cables. Mice, keyboards, network, and other connections are widely expected to be wireless. Sure, that laptop may be pretty mobile, but people hate having to connect and disconnect cables every time they want to move. They don't like the messy look of cables that often results at most desks even with "desktop" computers. They like to change the furniture layout in their office and the ports are no longer where they "should be" adding to the inconvenience and possible mess.
3. As a result of the above, many devices today do not come with a wired network interface installed. Without things like a wired network port, laptops/tablets can be made much thinner than if they had one installed. Battery life is extended by having once less device built in to keep powered. And from the manufacturers viewpoint, the less hardware they have to put into a device, the cheaper it is to manufacture.

2) Even the new 802.11ac with the right PCIe cards, will it match up to a 1Gbps fibre/copper connection?

3) Would a 802.11n 5GHz bridge be better than a fibre "bridge" for the 25 PCs on the other side?

These are ultimately both the same question but looking at different connections and the answer is the same for both. No. A wireless connection is not as good as a wired connection in almost all cases.

However the question shouldn't be "is it as good" but rather "is it sufficient to meet the client's needs (current and future)?" Having computers for every user with 64GB RAM, 4TB SSD storage (with RAID of course), the best CPU & GPU on the market and multiple large displays is probably certainly better than what they are currently using, but it is also probably overkill for what is actually needed.

Having a solid cabling plant providing the backbone that provides service to the APs themselves is important. Since they already have a reasonably solid cable plant, moderate upgrades and added wireless coverage/capacity would seem to be in order here.

WHY is cabling better than Wi-Fi? Is it the speed at which the data flows through the medium? Copper vs glass vs air? Does wireless have to jump through extra hoops to get the data sent?

You can definitely still get much higher speeds on copper/fiber than you can wireless. Generally speaking, fiber > copper > RF. But again, is it really speed the client is looking for?

Cabling is also more "stable" than wireless. 802.3 is much more mature and standardized. It isn't changing as quickly, is relatively simple in comparison and as a result doesn't run into many of the client inter-operability problems that can occur on wireless.

Cabling can also be more secure than wireless. RF energy sent out of a device is not limited to only reaching the intended device(s). Other devices can see and potentially make use of this information.

Yes, wireless has additional overhead and there are other limitations with how 802.11 operates.

Client now wants to install wireless APs everywhere (throwing out the existing cables) and bridges to new locations instead of fibre cables and CAT6 connections to static PCs because "it is faster, cheaper, future-proof and more efficient"

The the specific claims of the client:

• Faster : simply not true. Wired is currently faster in nearly all cases, even if you can use the full capabilities of 802.11ac on both the AP and client. This claim should be easy to refute.
• Cheaper : you may want to start by reading my answer posted to a similar question. While it is now almost three years old, many of the same principles apply. But if you are comparing providing brand new service to multiple end users, this is certainly true in some senses. Cabling is expensive, switch ports are expensive, and if you can serve multiple devices off of one (to an AP) then those costs are lower.
• Future-proof : again, true to a degree. Going back to my point #3 above, many devices no longer come with a network port. They expect wireless service to be available, so the request does take into account this need.
• More efficient : I guess this would depend on how one measures "efficiency." Much like statistics, if you change the "measure" you change which is more efficient.

Again, I would personally propose some sort of happy medium here. Provide the full wireless coverage the client desires, but also propose upgrades to the current infrastructure that will benefit both the additional wireless support and the existing wired connections.

There is no reason to "throw out" the existing network. Make use of it where it makes sense (printers, copiers, servers, shared storage, etc) and enable the client's end users to be more mobile by losing the wires.

Just make sure you do it right and provide the correct information along the way. You did say that finances weren't an issue, so if it performs accurately to what you told the client, has the problems you warned them may occur, and they aren't happy, they shouldn't be upset about paying you more to transition some or all of the devices back to the wired network.