Both X-Men & Doctor Who debuted in 1963. Next year they turn 50. Aside from borrowing ideas from each other, they've never officially crossed over. THIS ENDS NOW. The mythologies of both franchises are so rich that you'd never do either justice by just sticking to one era for each. Thankfully time travel is a viable option. I don't know what the plot would be, but there should be plenty of character beats like below:
The Doctor, Cable, Bishop, Marvel Girl, & Layla Miller discuss why none of their time travel experiences are consistent. Wolverine pits his Adamantium claws & healing factor against Daleks' Dalekanium shells & death rays. Romana mistakes Psylocke for a fellow Time Lady after meeting her Caucasian & Japanese bodies. Mr. Sinister & The Master team up for unethical superscience of the goatee-stroking variety. Shadowcat & Adric compete to see who could be a more obnoxious whizkid. Day of the Daleks & Days of Future Past merge into the grimdarkest alternate future possible. Warwolves eat the Slitheen. Apocalypse & Sutekh argue over which one of them was really worshipped as Set. Ace & Jubilee bond over their mutual love of blowing \"naughty word\" up. Mighty Jagrafess of the Holy Hadrojassic Maxarodenfoe gets into a literal & gruesome ratings war with Mojo. The Nimon decide to continue The Great Journey of Life in The Xavier School for Gifted Youngsters. Northstar & Emma Frost sucumb to the wiles of Captain Jack Harkness. Spiral is able to pilot the TARDIS thrice better than The Doctor. Toad finds a neo-Silurian to play tongue tag with. The Brigadier & UNIT must prevent the Earth from being annexed by the Shi'ar. Magnus Greel & Mr. Sin conquer the Morlocks. Omga escapes the antimatter universe into Shadow King's lair on the Astral Plane. Moira MacTaggert is revealed as a direct descendent of Jamie McCrimmon. Forge builds a better Sonic Screwdriver out of random bits of ephemera left on the curb in tense moment after The Doctor's is destroyed again. The Kandyman stalks Danger. Maggot's Eany & Meany are mistaken for Cybermats. No-Girl becomes the new owner of Morbius's patchwork body. Mystique impersonates all The Doctor's regenerations in a row. The Phoenix Force chooses the TARDIS as its new host. Vervoids & Brood merge into the most repulsive aliens possible. Rory Williams possesses an X-Gene. Davros & Prof. X have wheelchair races. K-9 & Lockheed become the multiverse's greatest mismatched buddy cop duo.