If the floor is not level, you'll have problems regardless whether you glue it or nail it. If the installer doesn't know that, I'd find somebody else.
If I understand you correctly, you're going to have both 5" & 31/4". Wouldn't that look odd.

Level is not a concern. No house is level. No house!
You want to make sure its Flat. Someone with experience needs to go over every single square Inch and find the high spots and low spots then they need to either be filled in or grinded down.

Has someone measured the moisture level in your slab? You can glue down solid to concrete but you need to take proper steps to ensure the slab doesnt have moisture issues and you need a Good moisture barrier!

Rayrose, I will be only having the 3.25" wide engineered wood floors (unless it is acceptable to install the 3" wide solid wood floors on my concrete slab) installed.

I installed the 5" wide BR-11 Triangulo (via floating over a Floor Muffler Ultra Pad) in September 2009. On 3-20-2013, my pipe burst on my water heater from my pressure valve regulator failing. Both the pressure valve regulator and the water heater have been replaced in 2013 to avoid future problems. The floors got damaged with board cracking and separating so the floor needs to be replaced.

Near the end of 2013, the insurance company settled with me but withheld depreciation on the new floors until I have a signed contract and I start my installation of new hardwood floors.

I had two dogs die at year end causing weeks of stress as well as looking at kitchens and then my tax season came.

I am now ready to do my floors to settle the insurance claim and renovate the kitchen another time.

The store I chose when the insurance company said to pick one store out of the 5 stores with the middle range estimate. I was told the insurance company was going to pay them directly. Then the estimator left and the new person had no record of this, and I had to send them what I had all over and then they found the other estimator's notes. They sent me a check net of the depreciation of the floor which they withheld. Now I wish I chose the highest price since it appears that the floor's cost will even be more due to moving the filing cabinets in the rooms downstairs and possibly having to fix any results from the water damage when the former floor is removed.

The store's main estimator who I was working with has left the store so the owner came by today wanting to install solid hardwood using a special glue. I will continue with another reply so this is not so long.

Gregmills, thank you for replying to my post.

In 2009, I had several installers take moisture readings and my floor was dry. BUT since 2009, I had the water damage from the water heater on 3-20-13 which damaged the 5" wide BR-111 Brazilian Cherry engineered wood floors which have not been removed and are over the Floor Muffler Ultra pad that they were floated on. I had to buy area rugs as the planks had cracked and lifted. I was waiting to have the insurance claim settled first before removing the floors. My little 6 lb Maltese got her foot caught costing me over $300 with the vet bill, X-rays and pain medicine. Thankfully nothing was broken when she was running and got her foot caught in the floor and was whimpering and carrying on. That is why I bought the inexpensive temporary small area rugs to cover many of the damaged areas until the insurance company settled with me.

I had chosen to install the same Brazilian Cherry Wood but now sold directly by Triangulo to stores rather than first sold to BR-111. I just want to change my width to 3.25" from 5". I would prefer a floating floor again as it felt like a solid wood floor but was not so hard on my feet.

The store had bought a large lot of 3" Solid Indusparquet Brazilian Cherry Hardwood so can give me a very good price on installing the solid wood by gluing it down using SIKA 2. I did look this product up and they are saying 3/4" solid hardwood can be glued directly to the concrete since it has a moisture barrier and good holding power but flexible.

I did call the manufacture of this wood today and Indusparquet will not warranty the solid wood unless it is nailed to plywood floors.

I have get to go to the store to discuss the estimate he prepared for me but I am feeling I need to tell him that I really prefer the 3.25" engineered wood downstairs and upstairs. In the summer time, the air conditioner keeps the humidity level down and the house is maintained at 36 - 40% humidity. In the winter time, the dry air is a problem with my forced hot air heat. I used humidifiers downstairs in the day time in my home office and upstairs at night. I have never had a problem with the 5" engineered wood floors until the water damage so I feel I am OK with the engineered wood floors. But when I go upstairs at night, it is very dry and I have to run the humidifiers on a long time to make my bedroom humid enough so I do not get nose bleeds. This is what I am afraid of with the solid wood. I am also afraid of the install failing downstairs where the concrete floor is not flat/level.

I filled the large cracks I found when the carpet was removed in 2009 before the installer arrived to install the floor. I will not use him again as he told me to use 2 less boxes so I changed my order and we ran out of wood and he never came back to finish the job when the wood arrived. I want someone to do the full job and charge me extra for moving the heavy cabinets. I have bought so many stackable crates since I will empty them. I have called moving companies to get prices and in case a store does not want to move the cabinets into my garage themselves and to put them back on the floors.

Gregmills, I have decided I am going to tell the store that I want the 3.25" wide Triangulo Engineered Brazilian Cherry Floors and not the solid 3" Indusparquet floors since I do have concrete floors and I do not want to void my warranty before I get to enjoy my floors and I can't afford to move all these cabinets again if there is a problem. Thank you Gregmills for your input which confirmed what I was thinking. I also wondered why he got such a good deal on this wood and if there could be a problem and then I have no warranty.

I am also going to get a few estimates to be sure I hire the right person. I chose this store last year when the insurance company told me to pick one of the 5 estimates and they would pay them directly. Then the insurance adjuster left my insurance company and the new person months later called me and told me they were sending me a check based on the store I chose less depreciation and will send me the balance when I get a contract signed. I have the money and I need to be sure who ever installs my floor is going to do a good job so I do not have to redo this floor again. I just need a contract with whoever I choose. I know going cheap is not always best so I want a fair price for the work done with someone that will do a quality job. In 2013, I got a price for the insurance company for the BR-111 5" wide but a separate estimate for the floor I thought I was going to use which was the Armstrong 3.5" wide 4MM Engineered wood flooring. But after paying for new samples in early 2014 as I heard the wood had been changed, the samples are not as nice as the 2009 samples I paid for and did not fit tightly together like the Triangulo. Due to these reasons, I feel I will be happiest with the Triangulo Engineered Hardwood Floors with the 3.2 MM of real wood over the plywood.

The store was going to float my wood in July 2013 when I got the estimate from the employee and they were the middle range price out of 5 estimates. I now see I should have given the insurance company just the highest estimate. I was working with a long-time employee there that left and now I am dealing with the owner of the store that wants to glue down products instead. I want to float the wood using the Floor Muffler Ultra again as my neighbor's glue down floor started to come up after a year that was Bruce's engineered hardwood floors bought and installed by Home Depot.