Got curious and ran a little test: 300 MP is SLIGHTLY denser than Li'l Gun, or at least that's how my present batches worked out. However, the difference ain't much, about 2%.
As far as burn-rate of various powders in this class, while burn-rate charts usually show H110/W296 as slower than Li'l Gun, all such charts are average approximations. Powders can and do switch burn-rates depending on the application. As an example, while H110 is slightly slower than Li'l Gun in the .44 Magnum, it's considerably faster in the .22 Hornet. Hodgdon's own handloading data for both cartridges shows this.
In Alliant's data for 300 MP the SINGLE rifle cartridge listed is the .22 Hornet. The only load listed is for the 40-grain Hornady V-Max, with 11.7 grains producing 2944 fps in a 24" barrel. I noticed this a couple years ago, and when Li'l Gun disappeared for a while I tried some 300 MP, as I had a couple pounds on hand.
Muzzle velocity was a LOT less than listed in my Ruger No. 1B, despite the 26" barrel, around 2750 fps, which normally means pressure is less. (This is probably due to the rather long throat.) So I did some experimenting.
For years I'd used the commonly listed load of 13.0 grains of Li'l Gun with 40-grain bullets in the Ruger. Muzzle velocity ran 2900-3150 fps, depending on the bullet and primer (more on that later). So I used case expansion to check comparative pressures between Li'l Gun and 300 MP, a valid technique as long as the same NEW cases are used for two different loads.
When using same charges of 300 MP and Li'l Gun with 40-grain bullets, case expansion was slightly less with 300 MP loads--and so was velocity. Around 13.5 grains of 300 MP was required to match the velocities of Li'l Gun in the Ruger Hornet, and accuracy was very similar.
At this point I knew 300 MP was a fine substitute for Li'l Gun in the .22 Hornet, and bought an 8-pounder. I chronograph-checked the new lot against the old, and muzzle velocity was within 20 fps.
Have just started experimenting with 300 MP in my new-to-me Brno K-Hornet, but so far it looks like a winner. But one other factor should be noted: A few years ago I ran a primer test in the Ruger .22 Hornet, using the 13.0 load of Li'l Gun with various primers from CCI 500 small-pistol (pistol primers are, of course, a common trick among long-time Hornet handloaders) to several popular small-rifle primers.
The definite winner was the CCI 450 small-rifle magnum primer, both in accuracy and velocity. This may seem odd, but for years the standard Hornet powders were Alliant 2400, IMR4227 and H110, which are relatively easily ignited--and charges are relative small, especially with the old 45-grain roundnose bullet.
In the Hornet, Li'l Gun and 300 MP are slow-burning powders, and like many spherical powders apparently burn better with a little hotter primer. I'm betting that 300 MP, CCI 450's and 40-grain bullets turn out to be a top combination in the K-Hornet, and that's the way things look after initial testing. But I haven't done enough experimenting to settle on a final load yet.
