When I check National Express tickets from London Luton to Gatwick airport online, I get 25.9 GBP per person price. Train for the same time is 27.10. There is no significant difference between bus and train. Should I expect to get cheaper price for the bus ticket directly in the airport?
As others have said, the coach is likely to become delayed and take longer. But I'll answer mostly about the train because it's what I'm most familiar with.
The trains from Luton Airport Parkway to Gatwick Airport are usually more reliable (though there are of course exceptions), but you'll have to catch a bus from the airport itself to the railway station, since Luton is not directly rail-served.
The main route by rail is a direct Thameslink train between the two stations. It relies on a two-track "core" which runs underground through the centre of London - and so if this track has problems, the entire service is likely to be disrupted. But this is relatively rare, and if it happens, usually they're able to get things sorted pretty quickly, unless it's a particularly serious problem.
If there is a problem in the core, you might find you're able to get an East Midlands Trains service to St. Pancras International, and change onto the London Underground Victoria Line to Victoria where you can pick up a Gatwick Express train non-stop to Gatwick. As far as I can see, your ticket will be valid for this. This will likely be slower and certainly less convenient than getting the direct Thameslink service, but it might be worth your while making a backup plan using this route in the unlikely event that there are problems with Thameslink.
The rail ticket you're looking up is what's known as a walk-up ticket, which means there's no advantage to buying it in advance, besides perhaps convenience - you're just as able to walk up to the station on the day and buy a ticket for the same price.
Most trains on this route are now Class 700 units. These are spacious and sparse inside, as they're optimised more for the shorter journeys. The seats are quite hard and not particularly well-padded, so if you like your seats well-padded then you might not appreciate these trains.
Bought bus ticket in the airport from Luton to London for 12 GBP. Earliest option was sold out so took the next one. From London to Gatwick used train for 13.4 which was faster and more convenient. All in all, if you didn't book bus ticket in advance and it is peak time, the better option is train.
I would expect any on spot price to be the same or higher than the pre booked price for the same service, with an added risk of no availability. While UK public transport fares are often regulated, there is no obvious reason to hold down the fare on this particular route below what the market will bear.