Bike fit - comparison of similar geometries
You can use bikegeo.net to visually compare frame sizes. You can also just compare the stack and reach figures. Stack and reach are explained in this road.cc article and shown below, but the definition also applies to MTBs.

I entered the measurements in bikegeo.net, using red for the Decathlon, green for the M Giant, and blue for the L. It is true that the large Giant is very close in frame stack and reach to your current frame. With the same spacer height and the same stem length, the medium Giant's handlebars will be a bit closer to you and a bit lower than on the Decathlon. You can, however, add spacers and change the stem.

MTB geometry has changed very substantially in the past 20 years or so. This article has an explanation, but basically, MTBs' head tube angles have become slacker, their top tubes longer, and their stems shorter. This has led to a lot of improvements in handling in technical terrain. The Decathlon has a steeper head angle and shorter top tube than the same size Giant. The article compared a bike from 2000 to a modern one, and it detailed some very substantial differences. That said, the Giant will handle a bit differently than the Decathlon, and I would assume for the better.
When you said that you were between frame sizes, I assume you meant that you were at the short end of the recommended height range for the L Giant. The height ranges are approximate. The correct size for you does depend on a number of factors, one of which is your leg length relative to your torso length. It would be much better if you could physically try out the intended bike in both sizes - you don't know if your current position on the Decathlon is good, although you could go and get a bike fit from a store (which is often worth paying for anyway, even though they can cost a bit). That said, the fit coordinates for the large Giant are closer to your current fit coordinates.
One other minor difference is that the Giant has a slightly steeper seat angle. To maintain your saddle position, you would probably want to put the saddle a bit further back on the rails of the Giant. The difference here should be minor unless your saddle is currently pushed all the way back right now.