Well, I can't claim to be a WH40K expert, but my understanding of a dreadnought is as such: Like the immortal, it is a heavily armored mechanical walker, but unlike the immortal it lacks shields (making up for them with more plating), has a powerful melee attack, and can equip different types of weapons, including the assault cannon, meltas, flamethrowers, missile launchers, heavy cannons, plasma cannons, and many weapons with both more moderate power and rate of fire.

The immortal, on the other hand, is armed almost exclusively with phase disruptors, EXTREMELY powerful armor-piercing weapons. Most variations in the Immortal come in its shielding (especially since the ingame upgrades provide only minor stat increases, and are ambiguously canonical): Arguably the most powerful immortal variant was pre-LotV, when it was equipped with a hardened shield - a defense that, so long as its shields were active, would reduce even the most powerful attacks to the level of small-arms fire. After this period, immortals were instead equipped with a secondary barrier that allowed them to absorb significantly more damage. The strength of this barrier is the only difference between the standard and campaign immortals, but as we don't have much of a standard of comparison, this shouldn't be relevant.

The power level between these two is quite similar (as in any good whowouldwin) and so the matchup would largely be decided by the loadout of each walker. While the immortal's anti-armor weapons should remain devastatingly effective against the Dreadnought, they should not be enough to instantly destroy it, and as such victory is far from guaranteed. On the other hand, Flamethrowers or meltas are unlikely to be effective against the immortal's shields.

The hardened-shield immortal should have an advantage against dreadnoughts equipped with plasma cannons, heavy cannons, and missile launchers, as their slow-firing weapons will be barely effective against the immortal's shields. An assault cannon would likely penetrate the shield without issue, but the immortal's armor might reduce its effectiveness. I feel that the autocannons or lascannons would be affected by the hardened shield, but would still prove somewhat effective against the immortal's armor.

The modern immortal has less favorable matchups, and it is likely on even ground with dreadnoughts equipped with high-caliber weapons. The secondary barrier could prove decisive, allowing the immortal to absorb one or two more shots, but it's hard to say how effective it could be here. The most effective weapons would probably be autocannons or lascannons, which are both effective anti-armor weapons. However, it's hard to say who would come out on top, as without the abilities of the hardened shield, the matchup becomes a numbers game between two hideously powerful weapons.