Its not whether its stabilised or not that matters, what matters is how fast the lens is, or put another way what is the f number. The lower the number the faster the lens, it will let in more light as the optics are larger, that way you will be able to up the shutter speed which should give sharper images.
You dont mention what f number the first lens has ? 300mm might sound very tempting but if the optics are inferior the other might be a better option.
Lenses that give a massive zoom option are usually a jack of all trades and master of none.
mine - (Nikon D3 with range of 2.8 lenses, none of which have VR, I just have steady hands
)